A piezoelectric sensor (2 nd order system) has a natural frequency of 500 Hz, a damping ratio of 0.2 and static sensitivity of 4 volts/kN. Determine (a) the time constant of this system; (b) the ringing frequency (rad/s) and the period (s) of the output signal if a step function is applied; (c) the amplitude (volts) of the sensor's steady output to a periodic function input at 1000 Hz of amplitude 10 kN.