ON23 P41 Q4 Critically Damped Pendulum | Oct/Nov 2023 | Cambridge A Level 9702 Physics

9702/41/O/N/23
A heavy metal sphere of mass 0.81 kg is suspended from a string. The sphere is undergoing small oscillations from side to side, as shown in Fig. 4.1.
The oscillations of the sphere may be considered to be simple harmonic with amplitude 0.036 m and period 3.0 s.
(a) State what is meant by simple harmonic motion.
(b) Calculate:
(i) the angular frequency of the oscillations
(ii) the total energy of the oscillations.
(c) The suspended sphere is now lowered into water. The sphere is given a sideways
displacement of +0.036 m from its equilibrium position and is then released at time t = 0.
The water causes the motion of the sphere to be critically damped.
On Fig. 4.2, sketch the variation of the displacement x of the sphere from its equilibrium position with t from t = 0 to t = 6.0 s
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why "displacement reaches final value of zero between t = 0.75 s and t = 3.0 s at the latest"?or how can know the time of critical damping?