- A particle \(P\) of mass \(m\) is attached to one end of a light elastic string of natural length \(l\). The other end of the string is attached to a fixed point on a ceiling. The particle \(P\) hangs in equilibrium at a distance \(D\) below the ceiling.
The particle \(P\) is now pulled vertically downwards until it is a distance \(3 l\) below the ceiling and released from rest.
Given that \(P\) comes to instantaneous rest just before it reaches the ceiling,
- show that \(D = \frac { 5 l } { 3 }\)
- Show that, while the elastic string is stretched, \(P\) moves with simple harmonic motion, with period \(2 \pi \sqrt { \frac { 2 l } { 3 g } }\)
- Find, in terms of \(g\) and \(l\), the exact time from the instant when \(P\) is released to the instant when the elastic string first goes slack.