Pendulum Definition and 1000 Threads

Homework Statement A particle is in the ground state of a pendulum of length ##L##. ##L## suddenly increases to ##4L##. Find the probability that the particle will be in the ground state of the new pendulum. Homework EquationsThe Attempt at a Solution What's this question even asking? So the...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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 =...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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-...

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...

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...

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...

What is the potential 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 =...

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...

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. <=>...

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...

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...

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 [SIZE="6"]a[SIZE="3"]abs = [SIZE="6"]a[SIZE="3"]rel + [SIZE="6"]a[SIZE="3"]u +...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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 ?

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...