Problem 2:A measurement system is to be designed such that the maximum amplitude of the output signal is not to exceed 125% of the amplitude of the input signal (assume the sensitivity of the system is K = 1 [V/V] ). The spring constant of the system is k = 122.5 [N/m] and the effective mass is m =0.1 [kg]. Determine the minimum allowable damping ratio (E) and the range of frequencies for which the dynamic error is limited to ±5% (i.e. 0.95 <= M(w) <= 1.05) when using this damping ratio.

Fig: 1