Question

A massive bird lands on a taut light horizontal wire. You observe that after landing the bird oscillates up and down with approximately simple harmonic motion with period T. You also notice that during the initial oscillations the maximum height the bird reaches above its position at landing is equal to the distance below its landing position at which the bird finally comes to rest, when all oscillations have stopped. In terms of only T and g, the acceleration due to gravity, estimate the magnitude of the vertical velocity v_0 that the bird had at the instant of landing on the wire.

Answer 1

V_0 = AW V_0 = A(2 pi/T) conserving energy mg(A) = 1/2 mV_0^2 (g)A = 1/2(Aw)^2 A = 2g/ w^2 A = g T^2/2 pi^2 V_0 = Aw V_0 = 2g/w V_0 = gT/pi