Example

The mass is displaced to the left from its equilibrium position through a small distance d and is released. The mass undergoes simple harmonic motion.
The graph shows the variation with displacement x from the equilibrium position of the kinetic energy of the mass.

Use the graph to
(a) determine the distance d and the greatest acceleration through which the mass was displaced initially,
(b) determine the period, frequency and angular frequency.
(c) determine the corresponding equations of displacement, velocity and acceleration.
(d) determine the corresponding equations of elastic potential energy and the total mechanical energy and sketch them on the graph above.
(e) determine the corresponding equations of kinetic energy, potential energy and total energy
[0.8m, 0.79 s, 1.26 Hz, 7.91 rad/s]
[ x= - 0.8 cos(7.91t), v= 6.32 sin(7.91t), a= 50 cos(7.91t)]
[KE = 2.6 sin 7.91²t, PE = 2.6 cos 7.91²t, TE =2.6 J]
[KE = 4.06 (0.8²-x²), PE = 4.06 x², TE = 2.6 J]
Using the model, this graph can be shown