What is Compound pendulum: Definition and 26 Discussions

A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing.
From the first scientific investigations of the pendulum around 1602 by Galileo Galilei, the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s. The pendulum clock invented by Christiaan Huygens in 1658 became the world's standard timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s. Pendulums are also used in scientific instruments such as accelerometers and seismometers. Historically they were used as gravimeters to measure the acceleration of gravity in geo-physical surveys, and even as a standard of length. The word "pendulum" is new Latin, from the Latin pendulus, meaning 'hanging'.

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  1. FEAnalyst

    Compound physical pendulum - max velocity

    Hi, I'm working on a simple benchmark problem for FEA. It's a pendulum initially positioned at an angle of ##45^{\circ}## and then subjected to gravity. I'm interested in the maximum velocity (when the pendulum is in the vertical position). So far, I've been using this formula: $$v=\omega \cdot...
  2. C

    Torque calculation for a compound pendulum

    I need to write an equation for Newton's second law for the above system, where k1=k2 (both springs are the same). The red line represents a bar with m=2kg, l=2m. I know that I*α = M1 + M2 + M3 If we displace the bar by x, we get the angle of displacement theta. M1=M2=-k*x I know that...
  3. TheBigDig

    Determine the moment of inertia of a bar and disk assembly

    I have been given an answer for this but I am struggling to get to that point $$ANS = 0.430\, kg \cdot m^2$$ So I thought using the moment of inertia of a compound pendulum might work where ##I_{rod} = \frac{ml^2}{12}## and ##I_{disc} = \frac{mR^2}{2}## (##l## is the length of the rod and ##R##...
  4. VVS2000

    Compound pendulum experiment to find the acceleration due to gravity

    In this experiment, I still can't figure out why the graph between time period and distance from point of oscillation is like that. Why does it first decrease and increase so steeply? I got the second part because it goes near the centre of gravity and time period becomes almost infinite there...
  5. E

    Two different answers for compound pendulum problem

    I completed this problem in two different ways, and wonder why they give different answers. Firstly, I calculate the moment of inertia of the system as I = 0.572 kg m^{2}, and the total torque acting on the system as 12.152 N. Thus I can apply the rotational analogue of NII to write...
  6. M

    Simple and Compound Pendulums

    Hi, I am having some trouble with the following question, any help would be appreciated 1. Homework Statement For a simple pendulum, T^2 is directly proportional to the length of the string (L) Why is this not true for a compound pendulum? Homework Equations T= 2pi sqrt(l/g) [/B]The...
  7. M

    Finding g from a Compound Pendulum Graph: A Step-by-Step Guide

    I am doing the compound pendulum experiment but I am stuck on how to find the value of g from the graph Here's a description of the compound pendulum: The compound pendulum AB is suspended by passing a knife edge through the first hole. The pendulum is pulled aside through a small angle and...
  8. Chrono G. Xay

    Kinetic Energy of Double Compound Pendulum and Parallel Axis

    Kinetic Energy of Double Compound Pendulum and Parallel Axis Theorem Hello, there. I have a project I'm working on where I need to be able to calculate the kinetic energy of what basically amounts a double compound pendulum. However, the pivot point of the second pendulum is not at the center...
  9. Dennydont

    What is the period of a compound pendulum?

    Homework Statement A compound pendulum consists of a thin rod of length 1.4 m and a disc of radius 0.2 m. The centre of the disc is attached to the end of the rod and the pendulum pivots about the opposite end of the rod. Both the mass of the rod and the mass of the disc are the same, each...
  10. A

    Possible sources of error in compound pendulum experiment?

    completing my advanced higher physics investigation - measuring acceleration due to gravity for the oscillating mass on a spring experiment so far I have included friction between the nail & oscillating rod as a possible source of error can anyone think of anything else? thank you very much...
  11. I

    Compound Pendulum Eniquiries

    a rectangular plate of length 300mm and depth 200mm, whose top left corner is attached to a wire of 200mm is dropped lengthways. What is the angular velocity of the plate and the speed of the corner opposite to the one the wire is attached to, just after the wire is pulled taut (it doesn't...
  12. G

    Experimental physics - simplified compound pendulum formula

    Homework Statement We've been given an assignment to work out a formula for the period time of a compound pendulum. This is right in the beginning of an introductory physics course which means we haven't covered inertia or torque yet. So we're just supposed to find an approximate relation...
  13. A

    Calculating Density and R of a Compound Pendulum: A Step-by-Step Guide

    Little help in compound pendulum Homework Statement there is an equilateral triangle T with sides of length B. Suspend this triangle from a pivot throught on of its corners, so that it is free to swing about this corner in the plane of the tringle. I want to ask how to compute the density...
  14. S

    Linearising compound pendulum equation

    Homework Statement Linearise T=2pi√(K^2 + h^2)/gh K is known constant This is a compound pendulum equation, I want to plot some kind of formula with variable T against some kind of formula with variable H in order to find g from the gradient. Homework Equations The Attempt at a...
  15. M

    Acceleration of a compound pendulum

    Homework Statement A uniform thin rod of mass M and length L is supported horizontally by two supports, one at each end. The acceleration of gravity, g, is constant and in the downward direction. At time t=0 the left support is removed. Find the downward acceleration of the center of mass at...
  16. R

    How to Measure G with a Compound pendulum

    For my Advanced Higher Physics Investigation i am measuring acceleration due to gravity. Having already done it with a simple pendulum my teacher says i have to do the same with a "Compound Pendulum". I was wondering how to do this and also how to make a compound pendulum with a steel rod...
  17. M

    Equations of motion for a compound pendulum

    Homework Statement To derive the equations of motion for a compound pendulum. Pendulum parameters are: mass M, mass moment of inertia= Ixx,Iyy,Izz,Ixy,Iyz,Izx, Euler angles theta, phi & psi and their time-derivatives theta_dot, phi_dot, & psi_dot, and coordinates of center-of-mass (x,y,z)...
  18. M

    Deriving Equations of Motion for Compound Pendulum with 3 DOF

    Can anyone help? I have to derive eq of motion of a compound pendulum with 3 rotational dof. I know how to do it, for simple pendulum (using Lagrangian's).
  19. T

    Determining g with a Compound Pendulum: Issues with Uncertainties

    Hi all! I'm currently doing an experiment using a compound pendulum trying to determine the value of g. I have a problem with my uncertainties: Error in period T: The period is measured with the use of a photo-gate of accuracy +/- 0.0001s. For each height i did 20 measurements from which i...
  20. E

    Why is my compound pendulum experiment not proving Rouths Rule?

    I'm having some trouble prooving a basic compound pendulum theory - my company makes a piece of kit designed to do just that. In a simple experiment involving a long thin bar which is set on a knife edge and allowed to swing freely I have been changing the length of the bar and measuring the...
  21. C

    How Does Mass and Pivot Position Affect a Compound Pendulum's Period?

    Homework Statement I am doing some coursework investigating a simple compound pendulum (in the form of a meter stick with holes drilled along it's length) and the effect of different variables on it's time period. I am using a stopclock to measure the time taken for 15 variations to...
  22. T

    Trouble modeling runner’s swing-leg as double compound pendulum.

    There is a problem in biomechanics that relates to a human runner’s gait (1) and how much power they consume. At each speed a runner chooses a Preferred Step Frequency or PSF (2). If an athlete tries to run with a step frequency that differs from their PSF at that speed, their oxygen...
  23. D

    Determining Best Value of k for Compound Pendulum

    Homework Statement I have calculated the value of the radius of gyration, k for a bar (and moment of inertia) and got three different values from three different methods. Now i need to determine which is the best value. I'm confused about how to do this, and how do i get the %uncertainty for...
  24. G

    Find g (gravity) on a compound pendulum

    1. A compound pendulum is arranged to swing about either of two parallel axes through two points O, O' located on a line through the center of mass. The distances h, h' from O, O' to the center of mass, and the periods \tau, \tau'of small amplitude vibrations about the axes through O and O' are...
  25. S

    Acceleration due to gravity using a compound pendulum experiment

    I am required to plot a graph of l(1+L^2/12l^2) on the x-axis and T^2 on the y axis.The graph must be a straight line through the origin.I got the following values for the l values on the x-axis .57,.47,.37,.27,.17 and corresponding values of T^2 2.46,2.52,2.56,3.24,8.12.As you can see my values...
  26. Reshma

    Simple pendulum, a conical pendulum and a compound pendulum?

    What is difference between a simple pendulum, a conical pendulum and a compound pendulum? In which category does a Foucault's pendulum fall in?