Problem #3 (6 points) shaker tables are often used at nasa goddard to simulate mechanical loading during rocket launches and thus test the structural integrity of satellite payloads during the launch process. a particular table at goddard provides a known periodic sinusoidal displacement that serves as an input signal to a sensor/device placed on top. this may be used to calibrate an accelerometer if known displacements/accelerations are provided at a known frequency. if the shaker table displacement d(t) is programmed to vary between 2 and 5 mm at a frequency of 100 hz: a) express theinput signal dit') as a fourier series, b) plot the signal in the time domain (matlab preferred, hand-sketch acceptable) from time t 0 to t 40 msec, clearly labeling all axes and pertinent specifications, and construct an amplitude spectrum plot c)