w7_harmonic - 1 Problem. Simple harmonic oscillator In this...

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1 Problem. Simple harmonic oscillator In this problem you will use one of the most important conservation laws in Physics, conservation of energy to calculate the period of a simple harmonic oscillator. The figure below displays a mass m , which is attached to a spring with a spring constant k . x unstretched stretched m m k k At t = 0 , the spring is stretched to a distance A from the unstretched state and released from rest. We then let is oscillate indefinitely (assuming there is no friction involved), and measure the displacement x ( t ) from the unstretched state as a function of time.We will find the period of this oscillatory system by solving a differential equation relating the displacement x ( t ) to its derivative, i.e., the velocity of the mass m . a) Finding the initial conditions : find the value of the position, x ( t ) , and velocity, dx/dt , of the mass m at the time t = 0 . b) Finding the
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This note was uploaded on 10/31/2011 for the course MATH 1910 at Cornell University (Engineering School).

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w7_harmonic - 1 Problem. Simple harmonic oscillator In this...

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