Physics A2 · Oscillations. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
During simple harmonic motion energy changes continually between kinetic energy and potential energy. At the equilibrium position the speed is greatest, so the energy is all kinetic. At maximum displacement the oscillator is at rest for an instant, so the energy is all potential.
If there are no resistive forces, the total energy stays constant. It is proportional to the square of the amplitude and to the square of the frequency.
Plotted against displacement, potential energy is a parabola with its minimum at x = 0, kinetic energy is the same parabola upside down, and the total is a horizontal line. Kinetic energy and potential energy each reach their maximum twice in every oscillation.
Students assume that at half the amplitude the energy is half kinetic and half potential. Energy depends on x2, so at x = ½x0 the potential energy is only ¼ of the total and the kinetic energy is ¾.
Answer: 0.032 J.
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