1. For a second-order instrument with a sensitivity of 0.35 V/(m/s), a = 10.5 F, a = 1 and a = 0.2143 H estimate the natural frequency, damping coefficient, and ringing frequency of the instrument. Plot the input and output signals for an input signal of F(t) = (4.4 m/s) U(t) in Excel. Determine the 90% rise time and settling time from the plot. Label the transient and steady parts of the curve. 2. For the second order instrument in problem 1, find M(o) and o (w) for the components of the input signal F(t) =4 sin(2(0.223)t) sin(2(1)t) + 0.5 sin(2(1.87)t). What is the resonance frequency of this instrument? Plot M() and (c) vs /n on two separate plots. List each component of F(t) and whether it will be transmitted, filtered, or augmented by the instrument.