A critically damped spring-mass system has undamped natural angular frequency ω₀=100 rad s⁻¹ and displacement x(t)=x₀(1+ω₀t) $e^(-ω₀t).$ The damping force is maximum at:
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Question

A critically damped spring-mass system has undamped natural angular frequency ω₀=100 rad s⁻¹ and displacement x(t)=x₀(1+ω₀t)e^(−ω₀t). The damping force is maximum at:

G1 Physics · Accepted Answer

The damping-force magnitude is proportional to |dx/dt|. For x=x₀(1+ω₀t)e^(−ω₀t), |v|=x₀ω₀²t e^(−ω₀t), which is maximum at t=1/ω₀=0.01 s. Hence option A.