All Problems

Mechanical Oscillations

Problem 4.40

A body of mass \(m\) fell from a height \(h\) onto the pan of a spring balance (Fig. 4.10 ). The masses of the pan and the spring are negligible, the stiffness of the latter is \(x\). Having stuck to the pan, the body starts performing harmonic oscillations in the vertical direction. Find the amplitude and the energy of these oscillations.

Reveal Answer
a=(mg/x)V1+2hx/mg,E=mgh+m2g2/2xa=(m g / x) V \overline{1+2 h x / m g}, \quad E=m g h+m^{2} g^{2} / 2 x