Pendulum Definition and 1000 Threads

  1. N

    Simple pendulum equation of motion

    Hi! I've been trying to find the equation of motion for the simple pendulum using x as the generalized coordinate (instead of the angle), but I haven't been able to get the right solution... Homework Statement The data is as usual, mass m, length l and gravity g. The X,Y axes origin can be...
  2. DavitosanX

    Homogeneous 2nd Order DE from spring pendulum

    I'm currently taking a Classical Mechanics course, and we're studying the lagrangian equation. After a few exercises, I thought I'd try to come up with the motion equations for a pendulum where the mass hangs from a spring. The resulting differential equations take a form that I don't really...
  3. T

    Simple Pendulum: The gradient of the graph of T^2 against length

    I've been asked to investigate the value of g. My graph shows that the gradient is around 4.4 as when the length was 0.27m, the squared time period was 1.18s (since this is a T2 against L graph). My question is, of course, why? If I am detecting g, which is 9.81 on earth, why did I get such...
  4. T

    Calculating the Period of a Simple Pendulum

    A simple pendulum is suspended from a ceiling 3.2m high and the bob height from the floor is measured to be 68cm. Calculate the period of small amplitude oscillations of the bob. I converted 68cm to 0.68m. The total length of the pendulum must be 3.2 - 0.68 = 2.52. When working with the...
  5. Yae Miteo

    Pendulum Velocity Homework: Find Mass's Speed at Bottom of Path

    Homework Statement A mass m = 5.5 kg hangs on the end of a massless rope L = 1.81 m long. The pendulum is held horizontal and released from rest. How fast is the mass moving at the bottom of its path? Homework Equations a_c = \frac {v^2}{r} F = ma v = v_o + at The Attempt at a Solution I...
  6. T

    Simple Pendulum Damping: Finding Amplitude and Energy Loss Rate

    Homework Statement Consider a simple pendulum (point mass bob) 0.55m long with a Q of 370. a) How long does it take for the amplitude (assumed small) to decrease by two-thirds? b) If the amplitude is 2.9cm and the bob has mass 0.22kg , what is the initial energy loss rate of the pendulum...
  7. P

    How to Find Velocity in a Cycloidal Pendulum?

    Homework Statement Cycloidal Pendulum, with x= RΘ+RsinΘ and y = -RcosΘ I need to find the Lagragian. Homework Equations L = T - V The Attempt at a Solution I just want to know how do I find the velocity so I can find T, which is 1/2 mv². I thought it would be dx/dΘ but it didn't...
  8. D

    MHB Natural frequency of a pendulum being lowered at 2m/s

    A heavy machine weighing \(9810\) N is being lowered vertically down by a winch at a uniform velocity of \(2\) m/s. The steel cable supporting the machine has a diameter of \(0.01\) m. The winch is suddenly stopped when the steel cable's length is \(20\) m. Find the period and amplitude of the...
  9. T

    Full solution for the simple pendulum

    Having recently completed a session on the simple pendulum in physics, I was curious as to what the solution to θ''+(g/l)sin(θ)=0 for θ(t) was sans the sin(θ)=θ simplification.
  10. P

    Physical Pendulum Formula Derivation

    Homework Statement A physical pendulum, consisting of a uniform rod (of mass M and length L) with an attached blob, can oscillate about an axis that goes through one end of the rod. The mass of the blob is also M. The distance of the blob to the rotation axis is x. The aim is to derive a...
  11. T

    Pendulum Period on Earth and Mars

    Homework Statement A pendulum has a period of 4.50s on Earth. What is its period on Mars, where the acceleration of gravity is about 0.37 that on Earth? (2 sig figs) Homework Equations T= 2Pi(L/g)^.5 The Attempt at a Solution first must solve for the length on earth L =...
  12. H

    Simple Harmonic Motion Pendulum, can we use PE=1/2kAmplitude^2?

    I was wondering if we can somehow use the formula Potential Energy = 1/2K(x(x=Amplitude))^2 for a pendulum if we are only given the angle of displacement? Would the problems normally just say the PE at the top of the pendulum is such and such, please find max Velocity, Or also the max...
  13. H

    Throwing baton modeled as inverted pendulum

    Homework Statement The juggler twirls a baton as high as she can into the air. To do this she applies a fast and powerful wrist flexion torque of T=70Nm. The baton will fly as high as possible when it leaves the girl's hand with its max take-off velocity. In order to maximize take-off...
  14. 2

    What is the tension in a pendulum string?

    Homework Statement Hi all! I was wondering what the tension is in the string of a pendulum, because I think sparknotes is wrong on this. Sparknotes says that: "Choose a coordinate system: We want to calculate the forces acting on the pendulum at any given point in its trajectory. It will...
  15. 2

    Why is a pendulum only simple harmonic motion for small angles?

    Homework Statement Hi all! I'm slightly confused about pendulums and simple harmonic motion. In my textbook, it says that a pendulum only exhibits simple harmonic motion when the angle is small (<10 degrees). I was wondering why this is, using equations if possible. Without the math, I think...
  16. mishima

    Counting uncertainty in pendulum experiment?

    Hi, I am confused about when the rule for counting uncertainty applies. I know for radioactivity experiments one expresses the uncertainty (error) in the decay count as the square root of the count. So if you counted n decays you would report an average rate of n \pm \sqrt{n} I was...
  17. D

    How Does a Pendulum Behave When Its Support Accelerates Horizontally?

    Homework Statement A pendulum is at rest with its bob painting toward the center of the earth. The support of the pendulum is moved horizontally with uniform acceleration a , and the pendulum starts to swing. Neglect the rotation of the earth. Consider the motion of the pendulum as the pivot...
  18. J

    Time period of a conical pendulum by D'Alembert's principle

    Homework Statement Finding the time period of a conical pendulum by D'Alembert's principle. The string is of a constant length and all dissipations are to be ignored. Homework Equations The time period of a conical pendulum is 2\pi \sqrt{\frac{r}{g\tan\theta}}. I need to arrive at this result...
  19. T

    Simple Pendulum in Elevator: Calculating Angular Amplitude with Acceleration

    Homework Statement A simple pendulum of length l is tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period T, and it has an angular amplitude β. Now at some time when the bob of the pendulum is at the mean position, the elevator suddenly starts...
  20. PhizKid

    Pendulum pulled through hole adiabatically

    Homework Statement A string with a lead ball of mass ##m## is slowly pulled upward through a small hole. Consider the work done on the system during this process and find the change in energy and the frequency of this pendulum during this "adiabatic process", assuming the amplitude of the...
  21. P

    How to Handle Integration Bounds in Quantum Pendulum Problems?

    Hi guys, I've been studying the problem of the simple, one-dimensional quantum mechanical pendulum of length \ell and mass m . We first apply the small-angle approximation which of course reduces the problem to the simple harmonic oscillator. This part is easy enough. However, we then...
  22. J

    Poincaré Sections of the double pendulum with Mathematica

    I need to plot a Poincaré map for a double pendulum where the string connecting one mass to the other is elastic with elasticity constant k and rest length s. The equations of motions are: \dot{\theta}_1= \frac{p_{\theta_1}}{m_1 r_1^2} - \frac{p_{\theta_2}}{m_1 r_1 r_2} \cos{(\theta _1-...
  23. matineesuxxx

    Double Pendulum With Acceleration

    Homework Statement You are holding a special pendulum with two masses m_1 and m_2 , instead of one, connected by a rope as shown in Fig. You lower the pendulum such that the tension in the rope between the two masses is half the weight of the bottom mass. Find the acceleration with which...
  24. R

    Newton's Laws: Analyzing Forces on a Pendulum in Introductory Physics

    I am working on HS Physics teacher certification, the study guide lists one the competencies as follow: ​"Identifies and applies Newton's laws to analyze and solve a variety of practical problems (e.g., properties of frictional forces, acceleration of a particle on an inclined plane...
  25. matineesuxxx

    Speed of conical pendulum at angle alpha to horizontal

    Homework Statement Assuming we know the length of the string L, radius of the swept out circle r, angle formed by string and centre of circle, \theta, and angle the swept out circle is to the horizontal, \alpha, what is the speed, v, of the mass if it is constant? picture...
  26. V

    Potential Energy of a Pendulum

    What is the potential energy of a pendulum at any point?
  27. V

    What is the equation for the kinetic energy of a pendulum at any point?

    Homework Statement I want to find the equation of the kinetic energy of a pendulum at any point. I know the initial angle it is released from but I am having trouble finding the velocity at any point to be able to find the kinetic energy at any point. Homework Equations θ =...
  28. BrainMan

    Kinetic and Potential energy pendulum problem

    Homework Statement A 3-kg mass is attached to a light string of length 1.5 m to form a pendulum. The mass is given a initial speed of 4 m/s at its lowest position. When the string makes and angle of 30° with the vertical, find (a) the change in potential energy of the mass, and (B) the speed...
  29. A

    Pendulum conservation of energy

    Please look at pictures. There is something really weird going on. They say the bob has to make a vertical circle. Then, in the solutions, they say that, for that to happen, speed at top must be greater than zero. BUT, since the only force acting is mg, that means that mg=mv^2/r. <=>...
  30. B

    Estimating Walking Speed w/ Ideal Physical Pendula

    Homework Statement Estimate your walking speed assuming that your legs are ideal PHYSICAL PENDULA. Estimate your walking speed by measuring how long it takes you to walk 10 m. Was your "pendulum" walking speed faster of slower than your "clocked" walking speed? Why? Homework...
  31. S

    I need the parametric equations for a simple pendulum

    This is for a personal engineering project. I need the parametric equations y(t) and x(t) for a very simple pendulum. Assume no friction, no forcing, no variation in gravity, a point mass, and the tether angle is significantly less than 30 degrees. It has been a while since I did differential...
  32. K

    Rotating pendulum. Find absolute acceleration

    Homework Statement I have to find current absolute acceleration in attached picture in points 1,2,3,4 and draw vectors. The picture is rotating pendulum. The rest data show attached picture: Homework Equations aabs = arel + au + acor acor=2*angular velocity X vrel The Attempt at a...
  33. A

    Finding the Center of Mass of a pendulum

    Homework Statement Assuming that the combined mass of the balls is greater than the combined mass of the cords, but that the cords do have some mass, where is the center of mass for the system shown below? Homework Equations None The Attempt at a Solution I tried approaching...
  34. L

    Solve SHM of a Pendulum: Calculate Length with T=1.2s & g=9.8

    Homework Statement A uniform steel bar swings from a pivot at one end with a period of 1.2 seconds. How long is the bar? Homework Equations T=2\pi\sqrt{L/g} The Attempt at a Solution I manipulated this equation to solve for L, giving me L=T^{2}g/4\pi^{2} Plugged in T=1.2 seconds...
  35. Radarithm

    Taylor 4.34 - Energy of a Pendulum

    Edit: Can someone change the name of the thread somehow? I accidentally posted it without changing the name. (Moderator note -- title updated.) Homework Statement The question is quite long so here is a picture: http://gyazo.com/dc917d1885b6ffebb0a39e2409af4d61 Homework Equations...
  36. I

    Simple Pendulum Amplitude Investigation: Graph and Uncertainty Analysis

    As part of a Physics experiment I have to investigate how the amplitude of a pendulum bob (attached to a string) varies with the number of oscillations it undergoes. The equation I have to work with is: (where t = the number of swings, A = amplitude after t swings, A0 = initial...
  37. S

    Simple Harmonic Motion Pendulum

    Homework Statement A small sphere with mass m is attached to a massless rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side so that the rod is at an angle θ from the vertical, and released from rest. When the pendulum rod is...
  38. G

    Solid pivoted pendulum attached to a spring - oscillation period?

    Homework Statement The figure shows a 200 g uniform rod pivoted at one end. The other end is attached to a horizontal spring. The spring is neither stretched nor compressed when the rod hangs straight down. What is the rod’s oscillation period? You can assume that the rod’s angle from vertical...
  39. S

    Accelerated mathemathical pendulum

    Homework Statement Mathemathical pendulum with mass ##m## on a line ##L## is moving with constant acceleration in xz plane, ##\vec{a}=(a_x,a_z)##. Let's consider only the oscillations in xz plane. Find stationary value of ##\theta ## and find the frequency of small movements around the...
  40. S

    Mathemathical pendulum with springs

    Homework Statement A body with mass ##m## is hanged on a line with length ##l## and attached to springs in point ##p##. Point ##p## can move only horizontally. In equilibrium position, non of the springs is deformed. Now let's give that body just a little push out of equilibrium position...
  41. P

    Finding the tension in a circular pendulum without radius or angle.

    Homework Statement Some kid is playing with a yoyo of mass m. The yoyo string is let out to length L, and is spun in a horizontal circle at a constant rate of ω. The yoyo string makes an angle of θ with the horizontal m = 39 grams = 0.039 kilgrams L = 46cm = 0.46m ω = 3 rads/sec...
  42. A

    What is the Missing Component in the Equation of Motion for the Asimov Pendulum?

    I am reading about the Asimov pendulum (see figure) The aceleration in spherical coordinates is ##\vec{a} =( R \dot{\theta}^2 - R \omega^2 \sin ^2 \theta) \hat{r} + (R \ddot{\theta} - R \omega ^2 \sin \theta \cos \theta ) \hat{\theta} + (2R \dot{\theta} \omega \cos \theta) \hat{\phi}## The...
  43. D

    MHB Mechanics-Conical pendulum, circular motion

    A particle of 100 grams is attached by two strings of lengths 30cm and 50cm respectively to points A and B, where A is 30cm vertically below B. Find the range of angular velocities for which the particle can describe horizontal circles with both strings taut. Take g as 10m/s^2 Answer Show...
  44. P

    Solve Torsional Pendulum Homework

    Homework Statement The same question was posted here before: https://www.physicsforums.com/showthread.php?t=73328 I'm struggling to come up with answers regarding the amplitude and energy in each case. The Attempt at a Solution For when the ring is dropped onto the disc when it is at rest, I...
  45. E

    Length of Pendulum with Variables Only

    Homework Statement A grandfather clock has a pendulum that consists of a thin brass disk of radius r and mass m that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in...
  46. M

    Simple pendulum with initial velocity

    Hi, I've attached a couple questions just because these are the type of questions I've had some difficulty solving since I don't recall addressing anything too similar too similar in the past (i.e., changing velocity and determining how the amplitude varies because of this). I know to go from...
  47. R

    Why doesn't mass of a pendulum effect its time period

    I'll jump straight to my query. If PE = mgh, and if the "m" is increased, the PE shall also increase. Neglecting friction, Total mechanical energy(TME) = PE + KE. Since PE increases, the total mechanical energy of the system shall also increase. At its equilibrium position, where PE = 0...
  48. R

    Plotting the graph of pendulum period versus length

    why do we square the value of T ( time period) while plotting the graph of effect on time period of a pendulum with change in its effective length ? also while deriving the formula of T=2∏√(l/g) why do we take T^2 = 1/g. Whats the need for squaring the time period ?
  49. R

    Collision - a ball and string form a pendulum

    Collision -- a ball and string form a pendulum... 1. A 1.0-kg ball is attached to the end of a 2.5-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point in its swing when it is moving horizontally, the ball collides elastically with a...
  50. W

    Hamiltonian of a pendulum constrained to move on a parabola

    Homework Statement The point of suspension of a simple pendulum of length l and mass m is constrained to move on a parabola z = ax^2 in the vertical plane. Derive a Hamiltonian governing the motion of the pendulum and its point of suspension. This is a two-dimensional problem...
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