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A damped harmonic oscillator of mass m has a natural frequency ω0, and it is tuned...

A damped harmonic oscillator of mass m has a natural frequency ω0, and it is tuned so that β = ω0.

a) At t = 0, its position is x0 and its velocity is v0. Find x(t) for t > 0

b)If x0 = 0.2 m and ω0 = 3 s−1 , obtain a condition on v0 necessary for the oscillator to pass through the equilibrium position (x(t) = 0) at a finite time t.

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