To determine the period and frequency of simple harmonic motion, we utilize the following formulas:

and

Period of Simple Harmonic Motion

The period ($T$) of simple harmonic motion is defined as the time required for one complete oscillation. It is measured in seconds ($s$). The formula for calculating the period is given by:

where:

• $m$ represents the mass of the object in kilograms ($kg$),
• $k$ is the spring constant measured in newtons per meter ($N/m$).

Importantly, the period is independent of the amplitude of the motion, meaning that changes in the amplitude do not affect the time taken for a complete cycle.

Frequency of Simple Harmonic Motion

The frequency ($f$) of simple harmonic motion indicates the number of oscillations that occur per unit of time. It is measured in hertz ($Hz$). The frequency can be calculated using the formula:

The frequency is directly related to the period and is inversely proportional to it. This relationship implies that as the period increases, the frequency decreases, and vice versa.

Summary

In summary, to compute the period and frequency of simple harmonic motion, we apply the formulas:

1. $T = 2\pi \sqrt{\frac{m}{k}}$
2. $f = \frac{1}{T}$

The period ($T$) represents the time for one complete oscillation and remains unaffected by the amplitude of the motion. Conversely, the frequency ($f$) quantifies the number of oscillations per unit time and is inversely related to the period.