Consider a simple harmonic oscillator with natural frequency, w =1 and the displacement from equilibrium of the mass is denoted by x. At t=0, the mass is released from x=1m with speed 2m/s. What is the magnitude of x at time, t=

Consider a simple harmonic oscillator with natural frequency, w =1 and the displacement from equilibrium of the mass is denoted by x. At t=0, the mass is released from x=1m with speed 2m/s. What is the magnitude of x at time, t=

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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(b) What is the maximum speed? I have attached the file thanks.
A meter stick of total length l is pivoted a distance d from one end on a friction-less bearing. The stick is suspended so that it becomes a pendulum. This is called a "physical" pendulum because the mass is distributed over the body of the stick. Assume the total mass is m and the mass density of the stick is uniform. The acceleration of gravity is g. Find T and V as functions of generalized coordinate θ and velocity ˙θ. Do this by considering the stick to be divided into infinitesimal parts of length dl and integrating to find the total kinetic and potential energy. Set up the Lagrangian and find the equation of motion.
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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.
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Consider the nonconservative mass-spring system governed by ï +2 +26x = 0, x(0) = 1, ż(0) = 4 (a) Find the solution z(t) and its derivative i(t), and evaluate x(7/5) and (7/5). (b) Calculate the total energy E (t) of the system when t = π/5. (c) Calculate the energy loss in the system due to friction in the time interval from t = 0 to t = π/5. no.
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