In Section 11.3, we discussed the total mechanical energy of a mass-on-a-spring oscillator. The result in Equation

Question:

In Section 11.3, we discussed the total mechanical energy of a mass-on-a-spring oscillator. The result in Equation 11.21 shows that the total energy is proportional to the square of the amplitude. Derive the corresponding results for the total mechanical energy of a simple pendulum and for a torsional oscillator and show that they are also proportional to the square of the amplitude.