Which frequency maximizes displacement?

A mass m = 0.50 kg, spring stiffness k = 50 N/m and viscous coefficient b = 6.0 kg/s form a linear oscillator. A sinusoidal force of fixed amplitude drives it after transients have decayed.

At what angular frequency is the displacement amplitude largest?

Organize the givens & assumptions

m = 0.50 kg
k = 50 N/m
b = 6.0 kg/s
Fixed force amplitude during the frequency sweep

Linear motion with constant parameters and positive viscous damping. The measured response is displacement amplitude, not speed amplitude or absorbed power.

A $\sqrt{28}\ \mathrm{rad/s}$
B $10\ \mathrm{rad/s}$
C $8\ \mathrm{rad/s}$
D $0$

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