An elastic string of natural length \(l\) is extended to length \(l + a\) when a certain weight hangs by it in equilibrium. This string and weight hang initially from the roof of a stationary lift. Then the lift descends, with acceleration \(f\) during time \(\tau\) and thereafter with constant speed. Prove that if \(f < \frac{1}{2}g\) the string never becomes slack. Given \(f < \frac{1}{2}g\), show that during the time \(\tau\) the amplitude of oscillation of the weight is \(af/g\) and that after the time \(\tau\) the amplitude is \(2af|\sin\frac{1}{2}n\tau|/g\), where \(n^2 = g/a\).
State the principles of conservation of linear momentum and conservation of angular momentum. Explain