1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50 N/m, and mechanical resistance 8.0 kg/s. The mass is initially released from rest with displacement 0.30 m from equilibrium. Determine the displacement x(t) as a function of time without assuming weak dissipation. Numerically compute all quantities. (b) The time for transients to become negligible is typically taken to be 5t, where the time constant t is the time required for the amplitude to decay to e-1 of its initial value. Taking the displacement amplitude to be approximately A = Xoe§t where xo = 0.30 m, (which holds for weak damping), determine the amplitude at time 5t.
1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50 N/m, and mechanical resistance 8.0 kg/s. The mass is initially released from rest with displacement 0.30 m from equilibrium. Determine the displacement x(t) as a function of time without assuming weak dissipation. Numerically compute all quantities. (b) The time for transients to become negligible is typically taken to be 5t, where the time constant t is the time required for the amplitude to decay to e-1 of its initial value. Taking the displacement amplitude to be approximately A = Xoe§t where xo = 0.30 m, (which holds for weak damping), determine the amplitude at time 5t.
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Transcribed Image Text:1(a) A damped simple harmonic oscillator has mass 2.0 kg, spring constant 50
N/m, and mechanical resistance 8.0 kg/s. The mass is initially released from rest
with displacement 0.30 m from equilibrium. Determine the displacement x(t) as a
function of time without assuming weak dissipation. Numerically compute all
quantities.
(b) The time for transients to become negligible is typically taken to be 5t, where
the time constant t is the time required for the amplitude to decay to e-1 of its initial
value. Taking the displacement amplitude to be approximately A
= 0.30 m, (which holds for weak damping), determine the amplitude at time 5t.
= Xoe¬Bt where xo
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