A seismic instrument like the one shown in Figure 2 is to be used to measure a periodic vibration of the object in motion with dynamic displacement y(t) = 2sin20nt +3sin60nt mm. a. Specify an appropriate combination of natural frequency and damping ratio such that the dynamic error in the output is less than 5%, With these values of natural frequency and damping ratio, Calculate the phase lag of the input signal. b. Determine an appropriate sample rate and sample period to minimize amplitude ambiguity in DFT method, and draw the amplitude spectra of the signal. c. Design an active RC low-pass first-order or second-order filter to eliminate aliasing frequencies, draw the circuit diagram, determine the cutoff frequency of filter, and give the values of the resistors and capacitors for your design. Spring Object in motion M Kelley Seismic mass Input motion Output transducer Damper N Im Figure 2 seismic instrument