What is Pendulum: Definition and 1000 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timekeeper, used in homes and offices for 270 years, and achieved accuracy of about one second per year before it was superseded as a time standard by the quartz clock in the 1930s.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. H

    What Are the Conservation Laws in a Pendulum Collision Problem?

    Homework Statement A stick of mass m and length l is pivoted at one end. It is held horizontal and then released. It swings down, and when it is vertical the free end elastically collides. Assume that the ball is initially held at rest and then released a split second before the stick strikes...
  2. G

    Coupled pendulum oscillation

    Homework Statement Consider 2 pendulums with the same length L, but 2 different masses Ma and Mb. They are coupled by a spring of spring constant k which is attached to the bobs (the masses). a) find the equations of motion b) find the frequencies and configurations of the normal modes...
  3. L

    Pendulum velocity at any given angle

    Trying to find an equation that will give me a pendulum bob velocity at any given angle if the pendulum is released from a 90° angle from it's equilibrium position. My parameters are as follows 9.8 (acceleration of gravity m/s^2) 1.397 (length of pendulum in meters) .138 (mass of...
  4. Conservation

    Net force on a Swinging Pendulum

    Hello everyone, Consider a weight tied to a string spinning in a horizontal circle. According to Newton's third law, the force of the string on the weight (inward) is opposite and equal to the force of the weight on the string (outward). If this is the case, how can there be a net...
  5. P

    Simple Harmonic Motion: Simple Pendulum

    If we apply the small angle approximation so that a simple pendulum can be considered to be under going SHM, what kind of potential energy would the pendulum bob be having? If the answer is gravitational potential energy, then we have a contradiction because this would mean that the bob would...
  6. A

    Relationship between frequency and length of pendulum

    Homework Statement We calculated times of the periods of varying pendulum lengths. (20cm, 40cm, 60cm, 80cm). Then the frequency was calculated for each length and then a frequency-length graph was made. Since the graph is an exponential relationship we graphed our values on a log-log chart...
  7. Saitama

    Shortening the length of pendulum

    Homework Statement Homework Equations The Attempt at a Solution I tried with the conservation laws. Angular momentum conservation won't work. To use energy conservation, I need the force pulling up the string but I don't have it. The force in the given case is tension but the tension...
  8. G

    Vertical Pendulum Questions

    Homework Statement A conical pendulum has length (L) 1.5m and rotates at 4ms-1. What is it's angle (θ) to the vertical? Homework Equations r = Lsinθ tanθ = v2/Lsinθg tanθsinθ = v2/Lg sinθsinθ/cosθ = v2/Lg sin2θ/cosθ = v2/Lg sin2θ + cos2θ = 1 The Attempt at a...
  9. carllacan

    Can you solve the pendulum with obstacles? Find the equation of movement!

    Homework Statement We have a pendulum, with length 4a. It is placed between two rounded obstacles (see image) described by x = a(θ+sinθ) and z = a(-3-cosθ), which disturb its natural movement. Find the equation of movement. https://www.dropbox.com/s/q1y4gzmnv0mm9c0/2014-01-27%2020.19.03.jpg...
  10. C

    Linear expansion of a pendulum

    Homework Statement A clock based on a simple pendulum is situated outdoors in Anchorage, Alaska. The pendulum consists of a mass of 1.00kg that is hanging from a thin brass rod that is 2.000m long. The clock is calibrated perfectly during a summer day with an average temperature of 19.5°C...
  11. L

    Physical pendulum in phase space

    Hi, I found out this paper http://www.pha.jhu.edu/~javalab/pendula/pendula.files/users/olegt/pendulum.pdf with this animation http://www.pha.jhu.edu/~javalab/pendula/pendula.files/users/olegt/pendula.html At first there is written there, that the area of possible states in some range...
  12. D

    What does the period of a normal pendulum depend on?

    Homework Statement If a simple pendulum has a metal bob having negative charge and is allowed to oscillate above a positively charged metallic plate will the time period increase, decrease, become zero or remain the same. Could you guys please give me an insight into what happens in the...
  13. T

    Gravitational Acceleration of Pendulum

    I am doing a lab report for IB Physics SL and I am supposed to use the slope of the period of a pendulum graphed against the length to find gravitational acceleration. I am trying to use the equation T=2∏√(l/g) but I'm not getting the right answer when I solve for g. (the answer is in s^2/m...
  14. C

    Kinetic energy of a pendulum in motion

    Homework Statement A trolley consists of an enclosed carriage of mass M supported by 4 wheels each of mass m/4. A simple pendulum consists of a bob of mass μ on a light rod of length l supported at a pivot attached to the roof; its motion is confined to a plane. a) Write down expressions for...
  15. Gh778

    Pendulum with not homogeneous attraction

    I would like to study a pendulum in 2D, not on Earth but only with one fixed mass attract a disk. Considered this fixed mass like a point. No friction on this theoretical study. The disk can move only around a part of circle. There are only 2 forces, F the attraction and N the force from wall...
  16. C

    Pendulum with Spring: Finding Position and Period

    Homework Statement A system consists of a spring with force constant k = 1250 N/m, length L = 1.50m, and an object of mass m = 5.00kg attached to the end. The object is placed at the level of the point of attachment with the spring unstretched, at position yi= L, an then is released so that it...
  17. S

    Pendulum: two masses hanged on a weightless line with a spring

    Homework Statement I have a system of two masses m hanged with lines l from the ceiling. We put a spring between the two masses. Find a general solution for this pendulum for small anglesHomework Equations The Attempt at a Solution Hmmm.. ##\sum M=0## ##J\ddot{\varphi _1}+mglsin\varphi...
  18. 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...
  19. C

    Pendulum Problem: Solve 100 Oscillations in 50cm Rod

    Homework Statement A pendulum is composed of a thin rod of length L = 50 cm, a moment of inertia of I = 0.2kgm2 with respect to its center and mass M = 400g. Attached to the bottom of the rod is a point mass (m = 200g). The pendulum swings in a vertical plane, attached by the top end to the...
  20. W

    Period of A Pendulum With Moveable Mass

    Homework Statement The figure below shows the pendulum of a clock in your grandmother's house. The uniform rod of length L = 2 m has a mass m = 0.8 kg. Attached to the rod is a uniform disk of mass M = 1.2 kg and radius 0.15 m. The clock is constructed to keep perfect time if the period of the...
  21. M

    Deriving Projectile Pendulum Formulas for Theoretical Speeds | Homework Help

    Homework Statement I need help deriving some formulas, specifically the theoretical speed of a bob at the bottom of a pendulum where the string is horizontal from the lower rod to the bob. Background / Introduction 1. A small weight at the end of a string of length, L, forming a simple...
  22. G

    Solve non-dimensionalized spring pendulum system on python

    Homework Statement I'm supposed to solve the spring pendulum numerically on python 2.7, using odeint. The system is supposed to solved for the y -direction and the x-direction in terms of time. In class we did this for pendulum DE, but that only had x as the dependent variable, this system has...
  23. D

    Physical pendulum thin rods problem

    Homework Statement Two identical thin rods, each with mass m and length L, are joined at right angles to form an L shaped object. This object is balanced on top of a sharp edge. If the L shaped object is deflected slightly, it oscillates. Find the frequency of oscillation. Here is a picture...
  24. heycoa

    Runge-Kutta Method for a double pendulum

    Hello, I am trying to program a double pendulum via the 4th order Runge-Kutta method and I cannot seem to be getting the right output. At first I used the Euler-Cromer method, but now I am aiming to make it more accurate. Homework Statement I have the equations of motion: d(omega)/dt and...
  25. deedsy

    Calculating Kinetic and Potential Energy for Simple Pendulum - Homework Problem

    Homework Statement A simple pendulum consists of a point mass m suspended from a fixed point by a weightless rigid rod of lengh l. The kinetic energy = 1/2*m*l^2*(dθ/dt)^2 The potential energy = -m*g*l*cosθ Calculate the time averages of the kinetic and potential energies over one...
  26. I

    Simple Harmonic Motion: Pendulum theory, trouble understanding

    Homework Statement So with pendulums in SHM, in my A level physics textbook (AQA Physics A), it shows a pendulum that has been displaced from equilibrium. It says that the restoring force is provided by the object's weight. Why isn't the restoring force provided by the tension in the string...
  27. K

    What is the Apparent Weight of a Pendulum on a Trapeze?

    Homework Statement I am trying to determine the apparent weight while on a trapeze/pendulum. So far, I have heard that the apparent weight is either: a. the Fnet of all vertical forces (aka Centripetal force) and b. it is the force of tension. I am not sure which it is. Homework Equations a...
  28. C

    Lab Project - build a physical pendulum with the smallest period

    Hi, I'm a student working with my group to create a lab for our final lab project. Me and my teammates are stuck on how we should begin to set up the project. I attached 4 photos, one of the pendulum setup, one of the model of our pendulum setup, and two others of the lab sheet guide. The...
  29. L

    What Is the Maximum Vertical Acceleration of a Pendulum?

    Homework Statement A pendulum has a length of 0.5m and an amplitude of oscillation of 8 degrees, what is maximum vertical acceleration Homework Equations X=Acos(\omega t + \phi) \omega =\frac{2\pi}{T} T=2\pi \sqrt{\frac{l}{g}}The Attempt at a Solution Taking the second derivative with respect...
  30. andyrk

    Pendulum in an accelerating car

    Homework Statement When a car is accelerating with a pendulum hanging inside it, then why does the pendulum get aligned with the vertical at an angle? Can you explain it without using the concept of pseudo force? I tried it but I was not able to get it. The Attempt at a Solution My Attempt...
  31. L

    Pendulum in non inertial frame

    Homework Statement A pendulum is placed on a rotating platform which rotates with angular velocity ω around an axis, at equilibrium the angle between vertical and pendulum is θ θ= 20 degrees ω= 10 1/s how far is the pendulum placed from the axis Homework Equations...
  32. J

    Calculating Maximum Height and Equilibrium Height of Pendulum with Wind Force

    Homework Statement A ball of mass m = 300 g is connected by a strong string of length L = 80.0 cm to a pivot and held in place with the string vertical. A wind exerts constant force F to the right on the ball as in the figure below. The ball is released from rest. The wind makes it swing up to...
  33. F

    Ballistic bullet pendulum conservation of momentum problem

    Homework Statement A 15 g bullet is fired into a 2.55 kg block that is hanging by a 2.0 m long string. The speed of the bullet is 425 m/s. Calculate the angle when the system reaches its maximum height?Homework Equations m1v1=(m1+m2)vf (1/2)mv^2=mghThe Attempt at a Solution (0.015 kg)(425...
  34. S

    Time period of a simple gravity pendulum

    Homework Statement Put of curiosity I have tried to derive a formula for the time period of a pendulum that oscillates under gravity. Below you can find my workings, which I have checked on wikipedia and the workings are practically identical. However I got stuck at one point, and this is...
  35. D

    Bullet Through Pendulum Bob-Inelastic Collision

    Homework Statement A bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges on the other side of the pendulum bob with half its original speed. Assume that the pendulum bob is suspended by a stiff rod of length L and negligible mass. What is the...
  36. N

    How Do You Calculate the Horizontal Force on a Pendulum?

    Homework Statement A 2.0 kg pendulum ball is pulled 30° from the vertical by a horizontal force Fpull. What is the magnitude of Fpull? Homework Equations F=ma The Attempt at a Solution I'm rather lost with this one - I'm not even sure how to classify it. Any help at all - even a point in...
  37. D

    Tough physics problem. Conical pendulum.

    Homework Statement Hey, thanks for taking a look at this. "The figure below shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass m...
  38. O

    Q Factor & Run Time of Pendulum

    Homework Statement Consider a small cuckoo clock in which the length of the pendulum is L, suspending a mass m with a period of oscillation T. The clock is powered by a falling weight (mass = M) which falls 2 m between the daily windings. The amplitude of the swing is 0.2 radians. (A)...
  39. K

    Simple Harmonic Motion (Pendulum)

    Homework Statement Two pendula of length 1.00m are set in motion at the same time. One pendula has a bob of mass 0.050kg and the other has a mass of 0.100kg. 1. What is the ratio of the periods of oscillation? 2. What is the period of oscillation if the initial angular displacement is...
  40. E

    Matching the double rod pendulum

    I'd like to understand how the double rod pendulum works and how it changes when a point mass is added to one of the rods. Especially I'd like to understand whether it's possible to match the two rods with the point mass so that the movement is stable under sinusoidal applied angular...
  41. N

    How Does Trigonometry Determine the Height in a Ballistic Pendulum?

    Homework Statement Using trigonometry and Fig. 2 in the ballistic pendulum write-up, show that the height h the pendulum rises after capturing the ball is given by: h=R(1-cosθ) Figure two is here: http://imgur.com/W9nvVZT Homework Equations h=R(1-cosθ) The Attempt at a Solution...
  42. 3

    Pendulum Rise from Release Point: 0.005 m

    Homework Statement You are given a pendulum composed of a 0.030 kg mass on the end of a 0.60 m long massless string. If the pendulum is moved 30° from the vertical and given an initial speed of 0.39 m/s tangent to the support string and away from the vertical, how much higher relative to the...
  43. T

    How high will the pendulum rise?

    Homework Statement You are given a pendulum composed of a 0.015 kg mass on the end of a 0.40 m long massless string. If the pendulum is moved 30° from the vertical and given an initial speed of 0.45 m/s tangent to the support string and away from the vertical, how much higher relative to the...
  44. Saitama

    How Does the Period of a Spinning Disk Pendulum Change?

    Homework Statement Find the period of a pendulum consisting of a disk on mass M and radius R fixed to the end of a rod of length l and mass m. How does the period change if the disk is mounted to the rod by a frictionless bearing so that it is perfectly free to spin?Homework Equations The...
  45. bananabandana

    Angular Frequency of Pendulum.

    Homework Statement How does a simple pendulum have a constant ω if it's velocity changes?Homework Equations (1) v=ωR (2) \omega=\stackrel{\sqrt{l}}{\sqrt{g}} The Attempt at a Solution Very confused about this. The pendulum bob is at a fixed distance from where it's attached (i.e R is...
  46. A

    Solving for Normal Modes in a Non Similar Coupled Pendulum

    Homework Statement (The picture is having trouble being directed so I attached it) Hey guys, I'm trying to figure out the normal modes of a pendulum with two different masses. The lengths of the strings are the same and the weight of the strings are negligible. I can easily find everything...
  47. E

    Tension in a Pendulum String - Oh my

    So I have one attempt left and want to make sure my answer is correct, so double checking me would be super awesome! You are given a pendulum composed of a 0.030 kg mass on the end of a 0.42 m long massless string. The pendulum is moved 25° from the vertical and released. Find the tension in...
  48. D

    How does the period of a pendulum affect its time measurement?

    Homework Statement A pendulum clock measures the time exactly if its period is T_0 . What time does the pendulum record in a time D , if its period becomes T ? Homework Equations I know that the number of oscilations of the pendulum in the time D is : N=D/T The Attempt at a Solution...
  49. A

    Conservation of Energy of an Interrupted Pendulum

    The studio explores the conservation of energy using the Interrupted Pendulum apparatus shown in (Figure 1). A ball is attached to a horizontal cord of length L whose other end is fixed. A peg is located at a distance d directly below the fixed end of the cord. The ball is released from rest...
  50. S

    Equation of Motion of a Inverse Pendulum on a Cart

    Homework Statement The nonlinear, inherently unstable inverted pendulum is shown in Figure 1.15. The goal is to maintain the pendulum angle θ(t) = 0 by using a feedback controller with a sensor (encoder or poten- tiometer) for θ(t) and an actuator to produce an input force f (t). The...
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