The above spring$-$mass system is at rest when the force $P(t)$ is applied, where

$P(t)=\frac{10N}{(\frac{t}{1}s{)}^4+1}$

The differential equation of the ensuing motion is

$y^{}=\frac{P(t)}{m}-\frac{k}{m}y.$

Solve the equations of motion numerically and determine the maximum displacement of the mass. Use $m=2\mathrm{.}5kg$ and $k=75\frac{N}{m}.$