[UPSC CSE 2013] Waves (Q32, 10M)

During an earthquake, a horizontal shelf moves vertically. If its motion can be regarded simple harmonic, calculate the maximum value of amplitude of oscillation so that the books resting on it stay in contact with it always. Take g=9.8\ \mathrm{m\,s^{-2}} and T=0.5\ \mathrm{s}.