Physics · Wave behaviour. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
An object moves with simple harmonic motion (SHM) when its acceleration is proportional to its displacement from the equilibrium position and always points back towards that position. A graph of acceleration against displacement is therefore a straight line through the origin with a negative gradient.
The amplitude is the maximum displacement. The period is the time for one complete oscillation. In SHM the period does not depend on the amplitude. For a mass on a spring it depends only on the mass and the spring constant. For a simple pendulum it depends only on the length and g.
Energy changes between kinetic and potential all the time. With no damping the total stays constant.
Students forget the square root. To double the period of a pendulum the length must be four times longer, and to double the period of a mass on a spring the mass must be four times larger.
Answer: About 0.80 m.
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