(a) Sketch a diagram of a simple pendulum performing simple harmonic motion and indicate positions of maximum potential energy and kinetic energy.
(b) A body moving with simple harmonic motion in a straight line has velocity, v and acceleration, a, when the instantaneous displacement, x in cm, from its maximum position is given by x = 2.5 sin 0.4 \(\pi t\), where t is in seconds. Determine the magnitude of the maximum (i) veloxity; (ii) acceleration
(c) A mass m attached to a light spiral is caused to perform simple harmonic motion of frequency
f = \(\frac{1}{2 \pi} \sqrt{\frac{k}{m}}\), where k is the force constant of the spring.
(i) Explain the physical significance of \(\sqrt{\frac{k}{m}}\).
(ii) If m = 0.30 kg, k = 30Nm\(^{-1}\) and the maximum position is 0.015m, calculate the maximum;
(i) kinetic energy
(ii) tension in the spring during the motion [g = 10 ms\(^{-1}\), \(\pi\) = 3.142]