All Problems Mechanical Oscillations
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.
4.38. (a) \(y=(1-\cos \omega t) w / \omega^{2}\) (b) \(y=(\omega t-\sin \omega t) \alpha / \omega^{3}\). Here \(\omega=\sqrt{x / m}\)