**Periodic motion** or harmonic motion is any motion that repeats at regular intervals. Simple harmonic motion is a sinusoidal function of time t.

Periodic motion is observed in mass on a spring, simple pendulum, molecular vibration etc.

The maximum displacement from equilibrium is known as the **amplitude** (always positive as only magnitude is considered).

One complete repetition of the motion is called a cycle. The duration of each cycle is the **period**. The **frequency** (f) is the number of cycles per unit time (t).

f=1/t.

For example, if a newborn baby’s heart beats at a frequency of 120 times a minute, its period (the interval between beats) is half a second as 60/120 = 0.5. Large frequencies means short periods.

Some motion is best characterized by the **angular frequency (ω)**. The angular frequency refers to the angular displacement per unit time and is calculated from the frequency (f) with the equation:

ω=2πf.

The phase of the motion is the argument of the cosine function. **Phase** varies with time, so does the value of the cosine function and the displacement of the wave. φ is called the phase angle or phase constant, it defines the position of the particle when t=0.

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**Practice Questions**

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Key Points

• Periodic motion (harmonic motion) repeats at regular intervals.

• Periodic motion can be described by amplitude, frequency and phase in a sinusoidal function.

• Frequency can be calculated by doing 1/t which is the number of cycles in that period of time.

Key Terms

**Amplitude**: distance between the rest position and the crest of the wave. Proportional to intensity.

**Period**: the duration of one cycle in a repeating event

**Frequency**: frequency is the number of occurrences of a repeating event per unit of time.

**Angular frequency (ω):** ω=2πf.

**Phase**: of the wave is the argument of the cosine function

**Periodic motion:** any motion that repeats at regular intervals.