Equation of motion Definition and 255 Threads

Let's say we have a sphere of charge of radius R, volume V, with total charge Q at t=0, so that we can express this as \rho ( 0 ) = Q/V. Now, if we were to "let go" of this clump of charge, the electrons would fly off due to the mutual repulsion. My question is how to model this, ie, how to...

Homework Statement The question involves a simple pendulum, I am given three equations (1), (2) and (3) of motion for the bob at latitude (fi) for the x, y and z components. the question then tells me to show that for small displacements meaning |theta|<< 1 (the angle between the string...

Homework Statement I'm trying to crudely approximately the distance individual masonry units fly when a blast load impacts a masonry wall. I'm a structures guy so I can calculate when the wall will failure, but I am having trouble with the calculus associated with the equation of motion. My...

How can we prove that (vf+vi)/2 is valid only for constant acceleration?? :confused:

Fashioned after the derivation of the equation of motion for a string with Neumann b.c in Zwiebach's a first course of string theory, I have derived the very similar equation using Dirchlet b.c. My result, in natural units, is X^{\mu}(\tau,\sigma)=X_{0}^{\mu}-2\alpha' p^{\mu}\sigma +\sum_{n\ne...

A transverse traveling wave is described by y(x,t)=0.6e2x-5tcos(5t-2x) for x and y measured in cm and t in s a) Show that y(x,t) satisfies the one-dimensional wave equation, and use this to deduce the wave speed. What is the direction of propagation? b)USe the work from part (a) to show...

Homework Statement I don't want to write the whole question as it is very long and I just have one query.. Basically the question involves a particle attached to three different springs which have fixed end points. In the question the mass of the particle is m, and the other constants used...

Homework Statement This isn't exactly homework, but this seemed like the right place for this question. I'm working on an add-on for Orbiter - the space flight simulator - and would like to be able to determine the equation of motion for an object traveling at an initial velocity (v0), with a...

Hi I'm using lagrange mechanics to try and come up with the equation of motion for the system in the image attached. Two pistons attached to a fly wheel, and are set 90 degrees apart on the wheel. 1 piston is pushed with a force F(t). The flywheel has inertia I. After using the lagrange...

Homework Statement So I've been staring at this problem for hours and I can't figure it out. The idea is to transform a second order equation of motion (depends on 'r' and 't') by the Hankel Transform. I think the purpose is to to avoid using separation of variables which tends to cause...

So I have a piston connected to a flywheel. If i push the piston with a force F, how does the equation of motion look? I'm not confident about putting inertias into the same equation as accelerations? F = ma F = I(theta'') The force is changing with time. EDIT: So i have just realized that...

I am wondering how is the third equatio of motion derived, I was reading a text on my physics course which it is very unclear how they exactly they arrived to this equation, knowing this from the book, using the equations for velocity and position, you can combine them to get 3 new equations of...

Pls help me to solve this..

Here's a question from a book: A particle of mass m is constrained to move on the surface of a sphere of radius R by an applied force $\mathbf{F}$(\thetha, \phi). Write the equation of motion. Now here is the answer, but there is something I don't understand about it: Using spherical...

1. All I need to do is derive the 4th equation of motion being v2= v02+2aD from the second (t=(v-v0)/a) and third (D=1/2at2+v0t). 2. In this case D= (Ending-initial distance) V0= Initial Veolocity 3. By having the second equation solved for t I could substitute it in an completely eliminate time...

I came across this from a book saying that: If all the co-ordinates and velocities are simultaneously specified, it is known from experience that the state of the system is completely determined and that its subsequent motion can, in principle, be calculated. Mathematically, this means that, if...

State the fundamental equation of motion for a particle of variable mass. A rocket of initial mass m0 is fired vertically, under the influence of a uniform gravitational field, and expels propellant at a constant relative velocity c downwards. The propellant is completely consumed after a...

Please guide me towards the "differential equation of motion" for the following 2 DOF Spring-damper system. And furthermore, if above system is in a uniform speed rotating frame, then what can be the effect on this system? Thank you very much.

Just reading about how if an operator commutes with the Hamiltonian of the system then its corresponding obserable will be a conserved quantity. my notes say that if \hat{L} commutes with the hamiltonian then the angular momentum will be conserved. this kind of makes sense but surely it's...

Homework Statement v = ui + v j u = cos(x)sin(y) v = -sin(x)cos(y) Find the circulation around randa to the square defined by: x = y = [-0.5*pi,0.5*pi] Homework Equations Is there a rule that says which sides on the square that get i and whics gets -i when you draw the square?

Homework Statement A particle of mass m is acted on by the forces as given below. Solve these equations to find the motion of the particle in each case. (a) F(x, t) = k(x + t2), with x = x0 and v = v0 = 0 when t = 0; (b) F(x', t) = kx^2 x', with x = x0 and v = v0 = 0 when t = 0; (c)...

Homework Statement A 1/4kg mass is attached to spring with stiffness of 4N/m. The damping constant for the system is 1 N-sec/m. If the mass is displaced 1/2 meter up and given an initial velocity of 1 m/sec upward, find the equation of motion. What is the maximum displacement that the...

Homework Statement I have coursework on rhe convolution integral, however i am struggling to find the equation of motion to start the whole thing off with. I will attach a picture of the problem, is is simply a cantilevered bar with a concentrated mass on the end and a damper. Homework...

Hi, I am trying to solve this problem here: http://img201.imageshack.us/img201/7006/springqo9.jpg We're supposed to find the equation of motion from the lagrangian and not Newton's equations. Attempted solution: L = T - U = \frac{I\omega^2}{2} + \frac{mv^2}{2} - \frac{kr^2}{2} I = m(r^2 +...

Hi, Been registered for a while here, but this is my first post, been using the forum as more of a resource before. I am going through some past papers, but I am faltering at 1 question. Homework Statement A particle moving along the x-axis with velocity v experiences a resistive force...

I'm just reading a basic physics tutorial, here is what it says in the section this post concerns:I don't get how the go from the second equation to the third equation (the one with Vo). I do know how to integrate, but what are they taking the integral with respect to?

Homework Statement The general equation of motion of a non-relativistic particle of mass m and charge q when it is placed in a region where there is a magnetic field B and an electric field E is m\bold{\ddot{r}} = q(\bold{E} + \bold{\dot{r}} \times \bold{B}) where r is the position of...

Homework Statement A mass m has speed v0 at the origin and coasts along the x-axis in a medium with force F(v). Use the chain rule of differentiation to write the equation of motion in the separated form m*v*dv/F(v)=dx. Homework Equations F(v)= -c(v^3/2) The Attempt at a Solution...

Homework Statement Uniform Rod of length 0.2m and mass 0.2kg pivoted at one end. THe other end of attached to a horizontal spring with spring constant 3.0N/m. The spring is neither stretched nor compressed when the rod is perfectly vertical. You can also assume that the force due to the...

Homework Statement A charged particle of mass m and charge q is free to move in the horizontal (x, y) plane, under the influence of the Coulomb potential due to another charge Q that is fixed at the origin. Find the Lagrangian and the differential equations of motion of the mass m, in...

Homework Statement two blocks each of mass m are connected by an extensionless uniform string of length l. one block is placed on a smooth horizontal surface and the other block hangs over the side the string passes over a frictionless pulley. describe the motion of the system when the mass of...

Homework Statement Find the equation of motion for a particle of mass m subject to a force F(x)=-kx where k is a positive constant. Write down the equation of motion as x''(t)=F/m. Then show that x(t)=Ceiwt is a solution to the equation of motion for any C as long as w has one of 2 possible...

Homework Statement The position of a particle moving along the x-axis is given by x = 6.0t^{2} - 1.0t^{3} , where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction? Homework Equations motion...

Homework Statement We have two particles, m1 and m2 at positions x1 and x2, and we want to come up with the equation of motion of particle m1 due to the gravitational field of m2 (position of m1 as a function of time). Homework Equations F=Gm1m2/r^2 F=ma The Attempt at a Solution...

It seems strange to me that in such a simple case as the following the equation of motion depends on the choice of metric! In flat space we have say: \partial^{\mu}\partial_{\mu}\phi=\frac{dV}{d\phi} Suppose \phi depends on space alone and we work in 1+1 dimension. then \eta_{\mu...

In the Heisenberg picture, we move the time dependence away from the states and incorporate them in the operators. That is, if we write the time dependent state in the Schrodinger picture as |\Psi(t)\rangle=e^{-iHt}|\Psi\rangle, then an expectation value for an operator Q at time t, which we...

Homework Statement A particle with a mass of 0.500 kg is attatched to a spring with a force constant of 50.0 N/m. At time t = 0 the particle has its maximum speed of 20.0 m/s and is moving to the left. (Use t as necessary.) (a) Determine the particle's equation of motion, specifying its...

The equation of motion for an observeable A is given by \dot{A} = \frac{1}{i \hbar} [A,H]. If we change representation, via some unitary transformation \widetilde{A} \mapsto U^\dag A U is the corresponding equation of motion now \dot{\widetilde{A}} = \frac{1}{i \hbar}...

Homework Statement A sin (wt + \Phi) = 0 Find A and \Phi Homework Equations Asin(wt)cos\Phi + Acos(wt)sin\Phi = 0 The Attempt at a Solution I was told to use magnitude to figure out A and something else to find \Phi in variable. I absolutely have no idea what to do... I found...

Question . A particle of mass m is constrained to move on the inner surface of a cone os semiangle alpha under the action of gravity. metion generalized co-ordinates and setup lagrangian and equation of motion.

Homework Statement A particle of mass m is constrained to move on the inner surface of a cone os semiangle alpha under the action of gravity. metion generalized co-ordinates and setup lagrangian and equation of motion. Homework Equations The Attempt at a Solution

Might there be a similarity between Dyson's equation and Heisenberg equation? (It's just a feeling, nothing based on arguments.) Both describe how a system (density matrix or Green's function) behaves in time. Both require knowledge of the intial system at time t=0 and the potential acting on...

Problem Outline: I'm trying to determine how to keep the distance between 2 cars on a (3D) roller coaster ride. Currently the front car moves away from the back car. My current implementation uses a second order differential equation to model the acceleration of the cars at time t. The...

Lagrange equation of motion (from Marion 7-7) A double pendulum consists of two simpe pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lenghts and have bobs of equal mass and if both pendula are confirned to move in the same plane, find...

I do not understand how people construct a suitable action which after variation will give the correct equation of motion. For example, the Einstein Hilbert action: S=integration[R d^4x] gives the equation of motion when varied with respect to [g_mu nu]. But no book I had read so far tells me...

Homework Statement The equation of motion of a mass m relative to a rotating coordinate system is m\frac{d^{2}r}{dt^2} = \vec{F} - m\vec{\omega} \times (\vec{\omega} \times \vec{r}) - 2m(\vec{\omega} \times \frac{d\vec{r}}{dt}) - m(\frac{d\vec{\omega}}{dt} \times \vec{r}) Consider the case F =...

Homework Statement A particle is dropped from rest, at the surface, into a tank containing oil The acceleration of the particle in the oil is a = g – kv where g is the gravitational acceleration and –kv being denoted by the resistance put on the particle by the oil. Solve for x as a...

In general how do you demonstrate that a given Lagrangian equation provides the correct equation of motion?

For a particle of mass m moving in a potential V(r) = -b/r^2 where the constant b>0 obtain the equation r = r(\phi} of the trajectory for the particular states of motion with total energy E = 0 and angular momenta such that \frac{L^2}{2m} < b SKetch the trajectory and discuss the motion for...

Please , I need to set up the equation for two springs. The first one is attached to a ceiling and has a constant k. The second one is attached at the tail of the first one and has a spring constant k'. If a mass m is attached to the second spring, How can I set up the equation for the system?