Two identical springs are used to set two blocks, P and Q, into separate simple harmonic motions along the same straight line. The masses of the blocks are equal and the spring constants are equal, but the amplitudes of vibration are different: AP=4cm and AQ=6cm. Answer the following:
(i) Write the expression for the total mechanical energy of a particle executing simple harmonic motion in terms of its amplitude.
(ii) Using this expression, determine the ratio EPEQ of the total mechanical energies of blocks Q and P.
(iii) Explain qualitatively why a change in amplitude affects the total energy even though the spring constant and mass remain the same.