A system with mass, $M=1000kg$ and $6$ springs as shown is subjected

to an initial upward displacement of $0\mathrm{.}040$ m at time $t=0.$

If $K1=5000\frac{N}{m},K2=4000\frac{N}{m},K3=5000\frac{N}{m},K4=4000\frac{N}{m},K5$

$=5000\frac{N}{m}$ and $K6=3000\frac{N}{m}.($Spring $2$ is nested in Spring $1$ and

Spring $4$ is nested in Spring $3).$

Ignore the phase delay angle $,$ and assume zero damping,

determine the following:

$($a$)$ The overall spring stiffness, Ke

$($b$)$ The oscillation frequency, fn$,$ in Hz

$($c$)$ Sketch the system displacement versus time graph.

$($d$)$ Sketch the velocity versus time graph.

$($e$)$ Sketch the acceleration versus time graph.

$($f$)$ Calculate the Max Displacement, Max Velocity and Max

Acceleration and the oscillation period and label these on

your graphs.

Hand written solution please