What is Pendulum motion: Definition and 23 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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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. D

    Derivation of time period for physical pendula without calculus

    TL;DR Summary: I'm stuck trying to find the equation for time period T of a physical pendulum without any calculus using torque. Hello all. I am currently writing my IB Physics HL IA (high school physics lab report). I am investigating the effect of length on the time period of a uniform rod...
  2. 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...
  3. anuttarasammyak

    Energy transfer and conservation cases for pendulum motion and EM wave

    Let me ask a very primitive question. To and fro motion of pendulum under gravity tells us potential energy + kinetic energy = const. At the top points potential energy: max kinetic energy :0 At the bottom point potential energy: 0 kinetic energy :max EM wave is usually illustrated as...
  4. Lo Scrondo

    Double pendulum motion (and Lyusternik-Fet Theorem)

    Hi everyone! I recently came across the Lyusternik-Fet theorem concerning closed geodesics on a compact manifold. For simplicity of description, take the 2-torus, and imagine it represents the configuration space of a double pendulum. For every pair of integers m, n (where m represents the...
  5. DracoMalfoy

    Measurement and Graphing. Dependence of a Pendulum on length

    For the experiment, we were to determine the relationship between two quantities through linearization after collecting measurements. To verify that P~L^1/2. and determine proportionality constant, C. P=C√L/g= (Cg^-1/2)(L^1/2) Materials used were a timer, string(The pendulum on length), and a...
  6. Alexanddros81

    Simple Pendulum motion - Numerical Integration

    Homework Statement The differential equation of motion for the simple pendulum can be shown to be ##\ddot {θ} = -(g/L)sinθ##. Given that L=9.81 m and that the pendulum is released from rest at θ=60deg, determine the time required for the pendulum to reach the position θ=0deg. Use Δt=0.10s, and...
  7. A

    Calculating error in pendulum motion

    Homework Statement I have to calculate the propagated error on g of pendulum. I pretty much measured the T of pendulum and now calculating g while increasing the number of cycles. Homework Equations I used the equation of propagated error and i included picture of it and my calculations. The...
  8. StrangelyQuarky

    How Do You Derive the Period of a Pendulum with Arbitrary Amplitude?

    Homework Statement A pendulum obeys the equation \ddot{\theta} = -\sin(\theta) and has amplitude \theta_0 . I have to show that the period is T = 4 \int_{0}^{\frac{\pi}{2}} \frac{d\phi}{\sqrt{1-\alpha \sin^2(\phi)}} where \alpha = \sin^2(\frac{\theta_0}{2}) 2. The attempt at a solution...
  9. tomdodd4598

    Pendulum with Pivot Moving in Horizontal Circle

    Homework Statement The problem is the following: Using a Lagrangian, find the equations of motion of a mass hanging from a massless string, with the pendulum pivot moving in a horizontal circle at constant angular velocity. I take the mass to be m, the length of the string L, the radius of the...
  10. D

    Pendulum Damping force effect on amplitude over time

    I am struggling with setting up a problem to solve for the change in amplitude of a pendulum affected by a damping force (presumable air friction) over a time period. The original amplitude of the pendulum is 1.4 m from the equilibrium on a 15 m massless wire with a 110 kg brass bob at the end...
  11. P

    Simple Pendulum in Free Fall: Surprising Motion and Video Evidence

    Homework Statement This is a 'random discussion' that I had today with a student; it is not out of a textbook, nor does the solution carry any weight at all (pls excuse pun).[/B] A simple pendulum is happily swinging back and forth attached to a pin in the wall of the lift, where the pin is...
  12. R

    Prevent Pendulum Motion with Winch & Cable

    Hi Clever People, Is there any method or gyro to prevent pendulum motion of an object when lowering it using a cable and a winch? I am doing a home projects and the motion is a big problem. Thank you in advance.
  13. S

    Pendulum motion and pythagorean theorem

    Homework Statement Show that the relation between the horizontal and vertical components of the ball's position is given by the equation: y = L - [(L^2 - x^2)^1/2] http://www.flickr.com/photos/94066958@N08/8553595522/in/photostream/ Homework Equations y = L - [(L^2 - x^2)^1/2]...
  14. J

    What is the Motion of a Bifilar Pendulum?

    Heyy guys, I have and EEI to do on a bifilar pendulum. Essentially a bifilar pendulum is acheived by two parallel strings instead of one. I have already built the device but don't know how the motion should be. Shourd it be farwards adn backwars? or side to side? or rotate? Thanks in advance:)
  15. A

    What is the connection between simple harmonic motion and pendulum motion?

    Homework Statement What is the connection between simple harmonic motion and pendulum motion? Homework Equations Harmonic motion period=T=2piroot(m/k) Pendulum motion period=T=2piroot(L/g) The Attempt at a Solution Conservation of momentum?? Thanks for any help!
  16. T

    Double Pendulum Motion: Plotting theta2 vs Time

    Hello all, I have written a python code implementing the Runge-Kutta fourth order method for higher orders to approximate the motion of a double pendulum. The problem I am having is that my plot of theta2 (angle of second rod) Vs time looks a little off and I am curious if I have it correct...
  17. G

    Archived Pendulum Motion (Simple Harmonic Motion)

    Homework Statement A 180 g mass on a 2.5m long string is pulled 6.6 degrees to one side and released. How long does it take for the pendulum to reach 2.7 degrees on the opposite side?Homework Equations omega = sqrt(g/L) theta = S/L theta(t) = A * cos(omega * t + phi) The Attempt at a...
  18. P

    Pendulum-Cart Motion: Solving for Functions of Time

    Homework Statement My teacher gave us a problem to work, but it's not assigned. He will probably give extra credit or something if we can do it... But anyway, I kind of want to solve it on my own, but I need a little help getting started. Ok, so let's say there is a cart of mass 'M' that...
  19. N

    Pendulum motion lagrange's equation

    i have been trying to solve this past exam problem, a simple pendulum of length l and bob with mass m is attracted to a massless support moving horizontally with constant acceleration a. Determine the lagrange's equations of motion and the period of small oscillations. here's what i solved...
  20. C

    Converting Circular Motion to Pendulum Motion: The Simple Crank-Slider Assembly

    Hi I want to build an upsidedown pendulum. My problem is what is the best/most used way of converting a circular motion (from the motor) to a pendulum motion. Thanks
  21. F

    Effects of Resistance & Speed on Coil Pendulum Motion in Magnetic Field

    How do resistance and speed of a coil in pendulum motion in a magnetic filed affect the induced voltage and the decay of Potential Difference? Details: Q1 When the speed of a coil is kept constant and a 3.3ohm resistor is added to the circuit of which the coil is a part of, the induced...
  22. T

    Understanding Tension in a Pendulum Motion

    1. I'm having trouble with the idea of tension in a pendulum. I've reasoned out my answers, but they're wrong. Am I missing a concept completely or am I overlooking a detail? Homework Statement The following questions deal with a pendulum in motion with angle not being its extreme end...
  23. D

    Simple Pendulum Motion and Physical Pendulum

    Homework Statement 1) Find the period of a pendulum 50 cm long when it is suspended in (a) a stationary elevator; (b) an elevator falling at the constant speed of 5.0 m/s; (c) an elevator falling at the constant acceleration of 2.0 m/s2; (d) an elevator rising at the constant speed of 5.0 m/s...