Yes, every periodic motion need not be simple harmonic motion explain the motion of the earth round the sun is a period motion, but not simple harmonic motion as the back and forth motion is not taking place.

Yes, when a ball is dropped from a height on a perfectly elastic surface, the motion is oscillatory but not simple harmonic as restoring force F ~ mg = constant and not F a - x, which is an essential condition for S.H.M.

The p.E of a particle executing S.H.M is given by,
Ep =\(\frac{1}{2}\)mw²y²
E_p is maximum when y = r = amplitude of vibration i.e., the particle is passing from the extreme position and is minimum when y = 0, i.e., the particle k passing from the mean position: The kinetic energy of a particle executing S.H.M. is given by;
E_k= mw²(r²-y²)
E_k is maximum when y = 0, i.e., the particle is passing, from the mean position and E_k is minimum when y = r, is the particle is passing from the extreme position.

(i) Let a spring be stretched between two points. Vibrations will set up in this string when it is disturbed, say from middle.
(ii) The figure given below shows that vibration set up in this string appears to be, similar to a half wave having wavelength \(\frac { \lambda }{ 2 } \)
Length of the spring l =\(\frac { \lambda }{ 2 } \)
λ = 2l
if T is tension in the string and m is mass per unit length of the string, then velocity of disturbance is given by,
v=\(\sqrt { \frac { T }{ M } } \)
v=\(\frac { wavelength }{ time } \)
=wavelength\(\times\)frequency
= λf
v1= 2l x f
f =\(\frac { v }{ 2l } \)
= \(\frac { 1 }{ 2l } \sqrt { \frac { T }{ M } } \)   \(\left[ \because v=\sqrt { \frac { T }{ M } } \right] \)

(i) The period of swing of simple pendulum will remains unchanged till the location of the center of gravity of the bob left after melting the ice remains at a fixed distance from the point of suspension.
(ii) If the centre of gravity of ice bob after melting is raised upwards, then the effective length of pendulum decreases and hence the time period of swing decreases. If the centre of gravity of ice shifts on lower side, the time period of swing increases.