Problem $3$: An SDF system is excited by a sinusoidal force. At resonance the amplitude of

displacement was measured to be $2$ in$.$ At an exciting frequency of one$-$tenth the natural

frequency of the system, the displacement amplitude was measured to be $0\mathrm{.}2$ in$.$ Estimate the

damping ratio of the system.

Hint: Recall that Rd $1$ for $\backslash$beta $<0\mathrm{.}2.$