Answered: Anisotropic Oscillator Consider a… | bartleby

Related questions

Question

Anisotropic Oscillator Consider a two-dimensional anisotropic oscillator
is rational (that is, ws/wy = p/q
4.
Prove that if the ratio of the frequencies w and wy
where p and q are integers with gcd(p, q) = 1, where gcd stands for greatest common
divisor) then the motion is periodic. Determine the period.
P

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Consider the solution tothe harmonic oscillator given above by x(t)=Ccos(wt−v) Prove tha tx(t0)=x(t0+2piw) In other words, the solution has the same value at time:t0 and at time:t0+2piw regardless of what value we have for ?0. The value 2piw is then the period T of the harmonic oscillator.
Suppose that you have a potential V (x) x2 + 6x – 8. Using a Taylor Series around Xo = 3, approximate the potential as a harmonic oscillator. O + (= – 3)? 7-2 (포-3)2 | (x – 3)? ||
An electron undergoes simple harmonic motion with the acceleration shown below: ax(t)=−amaxsin(2t/T) with amax=5839 ms2 and T=316 seconds. Assuming that the only motion is oscillatory (ignoring overall translation), what is the maximum speed of the electron? What is the amplitude of the electron's position?
Use the following transformation to solve the linear harmonic oscillator problem: Q = p + iaq, P = (p − iaq) / (2ia)
Consider the schematic of the single pendulum. M The kinetic energy T and potential energy V may be written as: T = ²m²²8² V = -gml cos (0) аас dt 80 The Lagrangian L is given by L=T-V, and the Euler-Lagrange equations for the motion of the pendulum are given by the following second order differential equation in : ас 80 = 11 = 0 Write down the second order ODE using the specific T and V defined above. Please write this ODE in the form = f(0,0). Notice that this ODE is not linear! Now you may assume that l = m = g = 1 for the remainder of the problem. You may still suspend variables to get a system of two first order (nonlinear) ODEs by writing the ODE as: w = f(0,w) What are the fixed points of this system where all derivatives are zero? Write down the linearized equations in a neighborhood of each fixed point and determine the linear stability. You may formally linearize the nonlinear ODE or you may use a small angle approximation for sin(0); the two approaches are equivalent.
Calculate the energy, corrected to first order, of a harmonic oscillator with potential:
Develop a Lagrangian for the double pendulum. You may need to make some assumptions to simplify the problem. You may also need to introduce some new variables to make the problem work. Make sure that is explained.