Question $6$

For the two dynamic systems in Figure $1,$ complete the following:

Vibrations

a$.$ Symbolically determine differential equations relating $\backslash ($ x$($t$)\backslash )$ to $\backslash ($ f$($t$)\backslash ).$

b$.$ Setting all coefficients to unity, determine their particular solutions for $\backslash ($ f$($t$)=\backslash$sin $(\backslash$omega t$)\backslash ).$

c$.$ Setting all coefficients to unity, determine the magnitudes and phases of the particular solutions as functions of frequency.

d$.$ Setting all coefficients to unity, plot both magnitudes versus frequency on the same graph and plot both phases versus frequency on another graph.