show that total energy of simple harmonic motion is conserved.
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Answer:
Energy Conservation in Simple Harmonic Motion
In simple harmonic motion, there is a continuous interchange of kinetic energy and potential energy. At maximum displacement from the equilibrium point, potential energy is a maximum while kinetic energy is zero. At the equilibrium point the potential energy is zero and the kinetic energy is a maximum. At other points in the motion the oscillating body has differing values of both kinetic and potential energy.
In this experiment displacement data (x(t)) is recorded and thus velocity data (v(t)) calculated using an ultrasonic motion detector and force data (F(t)) is recorded using a force sensor in one of the experimental set-ups on the next page.
Kinetic energy at all points during the oscillation can be calculated using the formula

Potential Energy at all points in the oscillation can be calculated using the formula

If mechanical energy is conserved the sum of the kinetic energy and potential energy should be constant at all times during the oscillation
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