simple pendulum problems and solutions pdf
OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. 877 0 0 815.5 677.6 646.8 646.8 970.2 970.2 323.4 354.2 569.4 569.4 569.4 569.4 569.4 frequency to be doubled, the length of the pendulum should be changed to 0.25 meters. We begin by defining the displacement to be the arc length ss. /Widths[314.8 527.8 839.5 786.1 839.5 787 314.8 419.8 419.8 524.7 787 314.8 367.3 WebClass 11 Physics NCERT Solutions for Chapter 14 Oscillations. Solution: In 60 seconds it makes 40 oscillations In 1 sec it makes = 40/60 = 2/3 oscillation So frequency = 2/3 per second = 0.67 Hz Time period = 1/frequency = 3/2 = 1.5 seconds 64) The time period of a simple pendulum is 2 s. WebAssuming nothing gets in the way, that conclusion is reached when the projectile comes to rest on the ground. If you need help, our customer service team is available 24/7. 2 0 obj /LastChar 196 /Name/F2 Phet Simulations Energy Forms And Changesedu on by guest /LastChar 196 WebMISN-0-201 7 Table1.Usefulwaverelationsandvariousone-dimensional harmonicwavefunctions.Rememberthatcosinefunctions mayalsobeusedasharmonicwavefunctions. /BaseFont/YBWJTP+CMMI10 As with simple harmonic oscillators, the period TT for a pendulum is nearly independent of amplitude, especially if is less than about 1515. 3 0 obj endobj Websome mistakes made by physics teachers who retake models texts to solve the pendulum problem, and finally, we propose the right solution for the problem fashioned as on Tipler-Mosca text (2010). 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 /LastChar 196 %PDF-1.2 351.8 935.2 578.7 578.7 935.2 896.3 850.9 870.4 915.7 818.5 786.1 941.7 896.3 442.6 sin << 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 A grandfather clock needs to have a period of Boundedness of solutions ; Spring problems . This paper presents approximate periodic solutions to the anharmonic (i.e. This part of the question doesn't require it, but we'll need it as a reference for the next two parts. That's a gain of 3084s every 30days also close to an hour (51:24). 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 A pendulum is a massive bob attached to a string or cord and swings back and forth in a periodic motion. /Type/Font 465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 The reason for the discrepancy is that the pendulum of the Great Clock is a physical pendulum. That's a loss of 3524s every 30days nearly an hour (58:44). A simple pendulum is defined to have a point mass, also known as the pendulum bob, which is suspended from a string of length L with negligible mass (Figure 15.5.1 ). 0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 Look at the equation below. An engineer builds two simple pendula. /LastChar 196 384.3 611.1 611.1 611.1 611.1 611.1 896.3 546.3 611.1 870.4 935.2 611.1 1077.8 1207.4 Solve the equation I keep using for length, since that's what the question is about. Exploring the simple pendulum a bit further, we can discover the conditions under which it performs simple harmonic motion, and we can derive an interesting expression for its period. Dowsing ChartsUse this Chart if your Yes/No answers are <> Solution: (a) the number of complete cycles $N$ in a specific time interval $t$ is defined as the frequency $f$ of an oscillatory system or \[f=\frac{N}{t}\] Therefore, the frequency of this pendulum is calculated as \[f=\frac{50}{40\,{\rm s}}=1.25\, {\rm Hz}\] endobj Web1 Hamiltonian formalism for the double pendulum (10 points) Consider a double pendulum that consists of two massless rods of length l1 and l2 with masses m1 and m2 attached to their ends. Example 2 Figure 2 shows a simple pendulum consisting of a string of length r and a bob of mass m that is attached to a support of mass M. The support moves without friction on the horizontal plane. Webpractice problem 4. simple-pendulum.txt. /Name/F6 323.4 877 538.7 538.7 877 843.3 798.6 815.5 860.1 767.9 737.1 883.9 843.3 412.7 583.3 /FontDescriptor 20 0 R 27 0 obj WebIn the case of the simple pendulum or ideal spring, the force does not depend on angular velocity; but on the angular frequency. D[c(*QyRX61=9ndRd6/iW;k %ZEe-u Z5tM Solutions to the simple pendulum problem One justification to study the problem of the simple pendulum is that this may seem very basic but its 298.4 878 600.2 484.7 503.1 446.4 451.2 468.8 361.1 572.5 484.7 715.9 571.5 490.3 by A simple pendulum with a length of 2 m oscillates on the Earths surface. 777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.9 885.4 806.2 736.8 What is the period of oscillations? The equation of period of the simple pendulum : T = period, g = acceleration due to gravity, l = length of cord. /Name/F7 13 0 obj PDF /Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 Since gravity varies with location, however, this standard could only be set by building a pendulum at a location where gravity was exactly equal to the standard value something that is effectively impossible. That way an engineer could design a counting mechanism such that the hands would cycle a convenient number of times for every rotation 900 cycles for the minute hand and 10800 cycles for the hour hand. [13.9 m/s2] 2. /Subtype/Type1 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000 %PDF-1.5 384.3 611.1 611.1 611.1 611.1 611.1 896.3 546.3 611.1 870.4 935.2 611.1 1077.8 1207.4 If the length of a pendulum is precisely known, it can actually be used to measure the acceleration due to gravity. 542.4 542.4 456.8 513.9 1027.8 513.9 513.9 513.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 <>>> WebFor periodic motion, frequency is the number of oscillations per unit time. The forces which are acting on the mass are shown in the figure. Websector-area-and-arc-length-answer-key 1/6 Downloaded from accreditation. : All of the methods used were appropriate to the problem and all of the calculations done were error free, so all of them. WebSimple Pendulum Calculator is a free online tool that displays the time period of a given simple. Which Of The Following Objects Has Kinetic Energy 3.2. >> Exams will be effectively half of an AP exam - 17 multiple choice questions (scaled to 22. /BaseFont/EKGGBL+CMR6 endobj 3 0 obj /FontDescriptor 17 0 R /Subtype/Type1 stream Solution Pendulum B is a 400-g bob that is hung from a 6-m-long string. Ap Physics PdfAn FPO/APO address is an official address used to WebThe simple pendulum system has a single particle with position vector r = (x,y,z). /Name/F1 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 481.5 675.9 643.5 870.4 643.5 643.5 546.3 611.1 1222.2 611.1 611.1 611.1 0 0 0 0 All Physics C Mechanics topics are covered in detail in these PDF files. <> When the pendulum is elsewhere, its vertical displacement from the = 0 point is h = L - L cos() (see diagram) Pendulum 2 has a bob with a mass of 100 kg100 kg. Physics 1120: Simple Harmonic Motion Solutions /FontDescriptor 11 0 R Half of this is what determines the amount of time lost when this pendulum is used as a time keeping device in its new location. /BaseFont/VLJFRF+CMMI8 /Parent 3 0 R>> endstream Energy of the Pendulum The pendulum only has gravitational potential energy, as gravity is the only force that does any work. - Unit 1 Assignments & Answers Handout. are licensed under a, Introduction: The Nature of Science and Physics, Introduction to Science and the Realm of Physics, Physical Quantities, and Units, Accuracy, Precision, and Significant Figures, Introduction to One-Dimensional Kinematics, Motion Equations for Constant Acceleration in One Dimension, Problem-Solving Basics for One-Dimensional Kinematics, Graphical Analysis of One-Dimensional Motion, Introduction to Two-Dimensional Kinematics, Kinematics in Two Dimensions: An Introduction, Vector Addition and Subtraction: Graphical Methods, Vector Addition and Subtraction: Analytical Methods, Dynamics: Force and Newton's Laws of Motion, Introduction to Dynamics: Newtons Laws of Motion, Newtons Second Law of Motion: Concept of a System, Newtons Third Law of Motion: Symmetry in Forces, Normal, Tension, and Other Examples of Forces, Further Applications of Newtons Laws of Motion, Extended Topic: The Four Basic ForcesAn Introduction, Further Applications of Newton's Laws: Friction, Drag, and Elasticity, Introduction: Further Applications of Newtons Laws, Introduction to Uniform Circular Motion and Gravitation, Fictitious Forces and Non-inertial Frames: The Coriolis Force, Satellites and Keplers Laws: An Argument for Simplicity, Introduction to Work, Energy, and Energy Resources, Kinetic Energy and the Work-Energy Theorem, Introduction to Linear Momentum and Collisions, Collisions of Point Masses in Two Dimensions, Applications of Statics, Including Problem-Solving Strategies, Introduction to Rotational Motion and Angular Momentum, Dynamics of Rotational Motion: Rotational Inertia, Rotational Kinetic Energy: Work and Energy Revisited, Collisions of Extended Bodies in Two Dimensions, Gyroscopic Effects: Vector Aspects of Angular Momentum, Variation of Pressure with Depth in a Fluid, Gauge Pressure, Absolute Pressure, and Pressure Measurement, Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action, Fluid Dynamics and Its Biological and Medical Applications, Introduction to Fluid Dynamics and Its Biological and Medical Applications, The Most General Applications of Bernoullis Equation, Viscosity and Laminar Flow; Poiseuilles Law, Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes, Temperature, Kinetic Theory, and the Gas Laws, Introduction to Temperature, Kinetic Theory, and the Gas Laws, Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature, Introduction to Heat and Heat Transfer Methods, The First Law of Thermodynamics and Some Simple Processes, Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency, Carnots Perfect Heat Engine: The Second Law of Thermodynamics Restated, Applications of Thermodynamics: Heat Pumps and Refrigerators, Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy, Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation, Introduction to Oscillatory Motion and Waves, Hookes Law: Stress and Strain Revisited, Simple Harmonic Motion: A Special Periodic Motion, Energy and the Simple Harmonic Oscillator, Uniform Circular Motion and Simple Harmonic Motion, Speed of Sound, Frequency, and Wavelength, Sound Interference and Resonance: Standing Waves in Air Columns, Introduction to Electric Charge and Electric Field, Static Electricity and Charge: Conservation of Charge, Electric Field: Concept of a Field Revisited, Conductors and Electric Fields in Static Equilibrium, Introduction to Electric Potential and Electric Energy, Electric Potential Energy: Potential Difference, Electric Potential in a Uniform Electric Field, Electrical Potential Due to a Point Charge, Electric Current, Resistance, and Ohm's Law, Introduction to Electric Current, Resistance, and Ohm's Law, Ohms Law: Resistance and Simple Circuits, Alternating Current versus Direct Current, Introduction to Circuits and DC Instruments, DC Circuits Containing Resistors and Capacitors, Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field, Force on a Moving Charge in a Magnetic Field: Examples and Applications, Magnetic Force on a Current-Carrying Conductor, Torque on a Current Loop: Motors and Meters, Magnetic Fields Produced by Currents: Amperes Law, Magnetic Force between Two Parallel Conductors, Electromagnetic Induction, AC Circuits, and Electrical Technologies, Introduction to Electromagnetic Induction, AC Circuits and Electrical Technologies, Faradays Law of Induction: Lenzs Law, Maxwells Equations: Electromagnetic Waves Predicted and Observed, Introduction to Vision and Optical Instruments, Limits of Resolution: The Rayleigh Criterion, *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light, Photon Energies and the Electromagnetic Spectrum, Probability: The Heisenberg Uncertainty Principle, Discovery of the Parts of the Atom: Electrons and Nuclei, Applications of Atomic Excitations and De-Excitations, The Wave Nature of Matter Causes Quantization, Patterns in Spectra Reveal More Quantization, Introduction to Radioactivity and Nuclear Physics, Introduction to Applications of Nuclear Physics, The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited, Particles, Patterns, and Conservation Laws, A simple pendulum has a small-diameter bob and a string that has a very small mass but is strong enough not to stretch appreciably. /Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 g Physics 6010, Fall 2010 Some examples. Constraints and endobj The SI unit for frequency is the hertz (Hz) and is defined as one cycle per second: 1 Hz = 1 cycle s or 1 Hz = 1 s = 1 s 1. For the next question you are given the angle at the centre, 98 degrees, and the arc length, 10cm. /FontDescriptor 20 0 R 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 643.8 839.5 787 710.5 682.1 763 734.6 787 734.6 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 x a&BVX~YL&c'Zm8uh~_wsWpuhc/Nh8CQgGW[k2[6n0saYmPy>(]V@:9R+-Cpp!d::yzE q This is a test of precision.). The comparison of the frequency of the first pendulum (f1) to the second pendulum (f2) : 2. To Find: Potential energy at extreme point = E P =? endobj . /Subtype/Type1 :)kE_CHL16@N99!w>/Acy rr{pk^{?; INh' /Subtype/Type1 Mathematically we have x2 1 + y 2 1 = l 2 1; (x2 x1) 2 + (y2 y1)2 = l22: <> 323.4 354.2 600.2 323.4 938.5 631 569.4 631 600.2 446.4 452.6 446.4 631 600.2 815.5 What is the cause of the discrepancy between your answers to parts i and ii? 460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1 0 0 0 0 0 0 0 0 0 0 0 639.7 565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 545.5 825.4 663.6 972.9 795.8 826.4 722.6 826.4 781.6 590.3 767.4 795.8 795.8 1091 The length of the cord of the first pendulum (l1) = 1, The length of cord of the second pendulum (l2) = 0.4 (l1) = 0.4 (1) = 0.4, Acceleration due to the gravity of the first pendulum (g1) = 1, Acceleration due to gravity of the second pendulum (g2) = 0.9 (1) = 0.9, Wanted: The comparison of the frequency of the first pendulum (f1) to the second pendulum (f2). 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.8 562.5 625 312.5 9 0 obj Compare it to the equation for a generic power curve. /FirstChar 33 593.8 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 /Subtype/Type1 36 0 obj Webconsider the modelling done to study the motion of a simple pendulum. /BaseFont/JMXGPL+CMR10 WebThe solution in Eq. 444.4 611.1 777.8 777.8 777.8 777.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 /Subtype/Type1 Here is a list of problems from this chapter with the solution. stream /FirstChar 33 Dividing this time into the number of seconds in 30days gives us the number of seconds counted by our pendulum in its new location. Problem (7): There are two pendulums with the following specifications. 18 0 obj Pendulum . /Subtype/Type1 /Type/Font 624.1 928.7 753.7 1090.7 896.3 935.2 818.5 935.2 883.3 675.9 870.4 896.3 896.3 1220.4 Pendulum 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 6 stars and was available to sell back to BooksRun online for the top buyback price of $ 0. Econ 102 Exam 1choices made by people faced with scarcity Single and Double plane pendulum <> >> >> Page Created: 7/11/2021. Oscillations - Harvard University 21 0 obj 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 >> endobj Period is the goal. The Pendulum Brought to you by Galileo - Georgetown ISD Projectile motion problems and answers Problem (1): A person kicks a ball with an initial velocity of 15\, {\rm m/s} 15m/s at an angle of 37 above the horizontal (neglect the air resistance). 33 0 obj /FontDescriptor 26 0 R PENDULUM WORKSHEET 1. - New Providence Now for a mathematically difficult question. What would be the period of a 0.75 m long pendulum on the Moon (g = 1.62 m/s2)? 692.5 323.4 569.4 323.4 569.4 323.4 323.4 569.4 631 507.9 631 507.9 354.2 569.4 631 WebAnalytic solution to the pendulum equation for a given initial conditions and Exact solution for the nonlinear pendulum (also here). Starting at an angle of less than 1010, allow the pendulum to swing and measure the pendulums period for 10 oscillations using a stopwatch. 14 0 obj PDF << Experiment 8 Projectile Motion AnswersVertical motion: In vertical N xnO=ll pmlkxQ(ao?7 f7|Y6:t{qOBe>`f (d;akrkCz7x/e|+v7}Ax^G>G8]S n%[SMf#lxqS> :1|%8pv(H1nb M_Z}vn_b{u= ~; sp AHs!X ,c\zn3p_>/3s]Ec]|>?KNpq n(Jh!c~D:a?FY29hAy&\/|rp-FgGk+[Io\)?gt8.Qs#pxv[PVfn=x6QM[ W3*5"OcZn\G B$ XGdO[. But the median is also appropriate for this problem (gtilde). In the following, a couple of problems about simple pendulum in various situations is presented. The most popular choice for the measure of central tendency is probably the mean (gbar). /Subtype/Type1 465 322.5 384 636.5 500 277.8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Adding pennies to the Great Clock shortens the effective length of its pendulum by about half the width of a human hair. /BaseFont/OMHVCS+CMR8 endobj Which answer is the best answer? 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 This PDF provides a full solution to the problem. Begin by calculating the period of a simple pendulum whose length is 4.4m. The period you just calculated would not be appropriate for a clock of this stature. 795.8 795.8 649.3 295.1 531.3 295.1 531.3 295.1 295.1 531.3 590.3 472.2 590.3 472.2 The rope of the simple pendulum made from nylon. Support your local horologist. Simple pendulum ; Solution of pendulum equation ; Period of pendulum ; Real pendulum ; Driven pendulum ; Rocking pendulum ; Pumping swing ; Dyer model ; Electric circuits; UNCERTAINTY: PROBLEMS & ANSWERS << Cut a piece of a string or dental floss so that it is about 1 m long. /Type/Font Pendulums Simple Harmonic Motion Chapter Problems - Weebly If displacement from equilibrium is very small, then the pendulum of length $\ell$ approximate simple harmonic motion. Simple Harmonic Motion << /Name/F5 Set up a graph of period vs. length and fit the data to a square root curve. if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'physexams_com-leader-2','ezslot_9',117,'0','0'])};__ez_fad_position('div-gpt-ad-physexams_com-leader-2-0'); Recall that the period of a pendulum is proportional to the inverse of the gravitational acceleration, namely $T \propto 1/\sqrt{g}$. 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 The period of a pendulum on Earth is 1 minute. xK =7QE;eFlWJA|N Oq] PB endobj Solution: The frequency of a simple pendulum is related to its length and the gravity at that place according to the following formula \[f=\frac {1}{2\pi}\sqrt{\frac{g}{\ell}}\] Solving this equation for $g$, we have \begin{align*} g&=(2\pi f)^2\ell\\&=(2\pi\times 0.601)^2(0.69)\\&=9.84\quad {\rm m/s^2}\end{align*}, Author: Ali Nemati The rst pendulum is attached to a xed point and can freely swing about it. /BaseFont/LFMFWL+CMTI9 277.8 500] /Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 24/7 Live Expert. 692.5 323.4 569.4 323.4 569.4 323.4 323.4 569.4 631 507.9 631 507.9 354.2 569.4 631 The period of a simple pendulum is described by this equation. /Name/F7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 706.4 938.5 877 781.8 754 843.3 815.5 877 815.5 Thus, The frequency of this pendulum is \[f=\frac{1}{T}=\frac{1}{3}\,{\rm Hz}\], Problem (3): Find the length of a pendulum that has a frequency of 0.5 Hz. xa ` 2s-m7k Solution: The period and length of a pendulum are related as below \begin{align*} T&=2\pi\sqrt{\frac{\ell}{g}} \\\\3&=2\pi\sqrt{\frac{\ell}{9.8}}\\\\\frac{3}{2\pi}&=\sqrt{\frac{\ell}{9.8}} \\\\\frac{9}{4\pi^2}&=\frac{\ell}{9.8}\\\\\Rightarrow \ell&=9.8\times\left(\frac{9}{4\pi^2}\right)\\\\&=2.23\quad{\rm m}\end{align*} The frequency and periods of oscillations in a simple pendulum are related as $f=1/T$. /Type/Font Compute g repeatedly, then compute some basic one-variable statistics. 888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 A simple pendulum shows periodic motion, and it occurs in the vertical plane and is mainly driven by the gravitational force. 351.8 935.2 578.7 578.7 935.2 896.3 850.9 870.4 915.7 818.5 786.1 941.7 896.3 442.6 /Subtype/Type1 Resonance of sound wave problems and solutions, Simple harmonic motion problems and solutions, Electric current electric charge magnetic field magnetic force, Quantities of physics in the linear motion. PDF What is the period of the Great Clock's pendulum? (Keep every digit your calculator gives you. 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 endobj endstream 472.2 472.2 472.2 472.2 583.3 583.3 0 0 472.2 472.2 333.3 555.6 577.8 577.8 597.2 endobj 413.2 590.3 560.8 767.4 560.8 560.8 472.2 531.3 1062.5 531.3 531.3 531.3 0 0 0 0 The pendula are only affected by the period (which is related to the pendulums length) and by the acceleration due to gravity. 525 768.9 627.2 896.7 743.3 766.7 678.3 766.7 729.4 562.2 715.6 743.3 743.3 998.9 Compare it to the equation for a straight line. Except where otherwise noted, textbooks on this site Tell me where you see mass. What is the period of the Great Clock's pendulum? 805.5 896.3 870.4 935.2 870.4 935.2 0 0 870.4 736.1 703.7 703.7 1055.5 1055.5 351.8 Jan 11, 2023 OpenStax. As an Amazon Associate we earn from qualifying purchases. >> Two pendulums with the same length of its cord, but the mass of the second pendulum is four times the mass of the first pendulum. Simple Harmonic Motion describes this oscillatory motion where the displacement, velocity and acceleration are sinusoidal. to be better than the precision of the pendulum length and period, the maximum displacement angle should be kept below about