Pendulum Definition and 1000 Threads

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...

A pendulum is released from rest at a distance y = H for the y = 0. What is the max velocity? \[ \frac{1}{2}mv^2 = mgh\Rightarrow v = \sqrt{2gh} \] where I assumed there was no air resistance. Would anything change if the system was in a vacuum?

Probably a stupid question...or possibly one with stupidly simple answer...Could this even work? I have this mechanism that generates electricity when you turn the crank (think Faraday's little doodad with copper wire and magnets) and am trying to figure out how to make this thing hands-free...

Homework Statement Two masses m_1 and m_2 (m_1 ≠ m_2) are connected by a rigid rod of length d and of negligible mass. An extensionless string of length l_1 is attached to m_1 and connected to a fixed point P . Similarly, a string of length l_2 (l_1 ≠ l_2) connects m_2 and P...

"Huygens' ingenious idea, which he put into practice, was to vary the eective length of the pendulum by allowing its cord to wrap partially around an obstruction as it swings" the coordinates of cycloid are: x=a(\theta -\sin \theta) y=a(\cos \theta +1) why in somes articles, they use the...

So I've always been confused about this. Suppose you have your normal pendulum: length L, mass m, and angle Θ. When you describe the potential energy PE = mgh, you must decide where to measure your h from. Throughout my years I've seen it measured from the mass to the 0 equilbrium point where...

Homework Statement A pencil of length l = 0.2 m is balanced on its point. How much time does it take to fall? Assume that the pencil is a massless rod and all of its mass is at the tip. To make the math easier, assume the small angle approximation. Homework Equations theta (double dot)...

I have completed a bottom driven pendulum that seems to have a preference to swing E/W. It is a 10kg bob on a 6M wire. The pivot is a tungsten carbide pin resting on a watch jewel. No matter how I start it it precesses at exactly the correct rate for 32 degrees latitude then stalls when it...

Homework Statement A box of mass M can slide horizontally on a frictionless surface. A simple pendulum of string length l and mass m, is suspended inside the block. Denote the coordinate of the centre of mass of the box by x and the angle that the pendulum makes with the vertical by θ . At t =...

Hello, question about the energy of a variable length pendulum. Suppose you have a pendulum in the standard sense where θ is the angle, and we let the length r be a function of time r = r(t). What is the energy of the pendulum? So far, I have determined that kinetic energy is =...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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)...

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...

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...