(i) When a pendulum clock gains time, it means it has gone fast, it makes more vibrations per day them required.
(ii) This shows that the time period of oscillations has decreased. Therefore, to correct it, the length of pendulum should be properly increased.

(i) When amplitudes of the vibrating pendulum is small then pendulum is small. Here the restoring force F = mg sin θ = mg θ = mgx/l .
(ii) Where x is the displacement of the bob and I is the length of pendulum. Hence F x x. Since F is directed towards mean position.
(ill) Therefore the motion of the bob of simple pendulum will be S.H.M. if θ is small.

S.H.M is the motion in which the restoring force is proportional to the displacement from the mean position and opposes its increase. Such a motion the displacement varies harmonically with time.

A phenomenon, process or motion, which repeats itself after equal intervals of time, is called periodic motion.
Examples:
(i) Heart beat of a person; period about 0.83s for a normal person.
(ii) Motion of earth around the sun; period is one year.

If a body moves to and fro repeatedly about a mean position it is called oscillatory motion.
Examples:
(i) Oscillations of a simple pendulum.
(ii) Vibrations of a mass attached to spring.