A particular load$-$cell sensor mounted to a machine is characterized by the

following parameters:

$m=4l{b}_m$

$k=800l\frac{b_f}{i}n$

$c=2l{b}_f-s\frac{ec}{in}$

If the machine upon which the sensor is mounted is subjected to the following input

excitation $F(t)$ :

where $A=100lb{b}_f$ and $=\frac{}{4}sec,$ determine the following:

$($a$)$ The frequency and phase angle spectrum plots for $F(t)$

$($b$)$ The undamped natural frequency of the sensor ${}_n(ra\frac{d}{s})$

$($c$)$ The critical damping of the sensor $c_{}(I{b}_f-s\frac{ec}{in})$

$($d$)$ The damping ratio of the sensor $$

$($e$)$ Plot the steady$-$state output produced by the sensor for input forcing frequencies

of $83ra\frac{d}{s},278ra\frac{d}{s}$ and $500ra\frac{d}{s}($You are expected to plot these using EXCEL,

MATLAB, etc. retaining at least $n=10$ harmonics and offer a short discussion $(2-$

$3$ sentences$)$ regarding the results$).$ Hint: program the resulting series solution in

EXCEL using VBA, or inside a MATLAB nested for loop structure.

PLEASE INCLUDE MATLAB CODE WITH GRAPHS