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Unformatted text preview: ¨ x + 10 ˙ x + 16 x = 0 (a) Find the damping constant b and the spring constant k . Is the harmonic oscillator under, critical, or overdamped? (b) At time t = 0 the particle is projected from the point x = 1 towards the origin with a speed u . Find an expression for x ( t ). (c) At what time t will the particle pass through the origin? How large must u be to ensure that this happens? 5. The equation of motion for a driven harmonic oscillator given by m ¨ x + b ˙ x + kx = F cos( ωt ) has the steady state solution x = D cos( ωtφ ) where the amplitude D and the phase φ are completely determined for the system. (a) Find the value of ω where the average potential energy h U i is maximum. (b) Find the value of ω where the average kinetic energy h K i is maximum. (c) Are your answers in part (a) and (b) the same? Discuss. (d) Find an expression for the average total energy h E i . 2...
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 Spring '10
 RogerMelko
 Kinetic Energy, Mass, asymptotic velocity, particular harmonic oscillator

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