1 problem found
The string \(AP\) has a natural length of \(1\!\cdot5\!\) metres and modulus of elasticity equal to \(5g\) newtons. The end \(A\) is attached to the ceiling of a room of height \(2\!\cdot\!5\) metres and a particle of mass \mbox{\(0\!\cdot\!5\) kg} is attached to the end \(P\). The end \(P\) is released from rest at a point \(0\!\cdot\!5\) metres above the floor and vertically below \(A\). Show that the string becomes slack, but that \(P\) does not reach the ceiling. Show also that while the string is in tension, \(P\) executes simple harmonic motion, and that the time in seconds that elapses from the instant when \(P\) is released to the instant when \(P\) first returns to its original position is $$ \left(\frac8{3g}\right)^{\!\frac12}+ \left(\frac3 {5g}\right)^{\!\frac12} {\Big(\pi - \arccos (3/7)\Big)}. $$ \noindent [Note that \(\arccos x\) is another notation for \(\cos^{-1} x\).]