Problem 4.38

A body of mass $m$ is suspended from a spring fixed to the ceiling of an elevator car. The stiffness of the spring is $x$. At the moment $t=0$ the car starts going up with an acceleration $w .$ Neglecting the mass of the spring, find the law of motion $y(t)$ of the body relative to the elevator car if $y(0)=0$ and $\dot{y}(0)=0 .$ Consider the following two cases: (a) $w=$ const; (b) $w=\alpha t,$ where $\alpha$ is a constant.