15.1: Mouvement harmonique simple

Simple harmonic motion is the name given to the oscillatory motion of a system where the net force can be described by Hooke's law; such a system is called a simple harmonic oscillator. If the net force can be described by Hooke's law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position. We can use the equation of motion to derive equations for the period and frequency of a simple harmonic oscillator.

The period of a simple harmonic oscillator is given by

Because frequency and period are inversely related, the frequency of a simple harmonic oscillator is

Note that neither period nor frequency has any dependence on amplitude, and the SI unit for frequency is hertz.

Let's consider two examples of when we might calculate frequency and period: (a) A medical imaging device produces ultrasound by oscillating with a period of 0.400 μs. What is the frequency of this oscillation? (b) The frequency of middle C on a typical musical instrument is 264 Hz. What is the time for one complete oscillation?

Both can be answered using the inverse relationship between period and frequency. Substituting the given value of period in the frequency expression, the frequency of oscillation is found.

Similarly, by substituting the given value for the frequency into the time period expression, the time for one complete oscillation is obtained.

This text is adapted from Openstax, College Physics, Section 16.3: Simple Harmonic Motion: A Special Periodic Motion and Openstax, University Physics Volume 1, Section 15.1: Simple Harmonic Motion.