A block of mass m attached to an ideal spring performs simple harmonic motion of amplitude A and angular frequency ω along a straight line. Answer the following questions:
a. (i) Write the standard mathematical expressions for (a) kinetic energy, (b) potential energy, and (c) total mechanical energy of the block in terms of its instantaneous displacement x from the mean position.
b. (ii) State the numerical values (in terms of the total mechanical energy) of the kinetic and potential energies when the block is (a) at the extreme position and (b) at the mean position.
c. (iii) Name the physical quantity that remains constant throughout the motion and specify its value in terms of the given quantities.