Physics 340 Fall 2003 Exam 1 25 points each 1.A simple harmonic oscillator has period T = 1 second. Its displacement is given by sin( )xatwf=+If the oscillation started at t = 0 from initial position x0= 0.5 m with initial velocity v0= πm/s, find φand a. 2.A particle of mass m slides freely on a frictionless parabolic track under the influence of gravity. Use g =10m/s2. The shape of the track is 2()0.1 metersyxx=a.What is the position of stable equilibrium? b.The mass is displaced a small distance from equilibrium and let go. Show that the motion is simple harmonic oscillation and find the angular frequency. c.Say the track actually has frictional forces given by 2Newtons30xym dxFdtF=-=In this case what is the angular frequency of the damped motion?
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