A 0.30kg block slides without friction on a horizontal surface and is attached to a spring with force constant 55Nm−1. Initially the spring is compressed 0.050m relative to equilibrium. At that instant the block is given a brief push toward the equilibrium position, imparting an additional speed of 1.20ms−1 to the block.
(a) Calculate the total mechanical energy of the block–spring system immediately after the push.
(b) Determine the amplitude of the ensuing simple harmonic motion.
(c) Find the maximum speed attained by the block during the motion, and calculate the time elapsed from the moment of release until the block first reaches this speed.