Q.The equation of displacement of a particle executing simple harmonic motion is y = sin(12πt + π/4). Frequency of the particle is (A) 8 Hz
(B) 12 Hz
(C) 6 Hz
(D) 4 Hz

Frequency and Period: The Rhythm of Repetition

Imagine a child on a swing, going back and forth. Each full cycle — forward, backward, back to the start — takes a certain amount of time. That time is the period. Now count how many such cycles happen in one second — that count is the frequency. Frequency and period describe the same repeating rhythm, just viewed from two different angles.

Everyday Intuition

Think of your own heartbeat. At rest, your heart beats roughly once every second. The period is about 1 second — the time between one beat and the next. The frequency is about 1 beat per second — how many beats occur in that same second.

If your heart speeds up, the period shrinks (less time between beats) and the frequency rises (more beats per second). Slow the heart down, and it's the reverse.

Precise Definitions

Period ($T$) — the time taken to complete one full cycle of a repeating event, measured in seconds (s).

Frequency ($f$) — the number of complete cycles occurring per unit time, measured in hertz (Hz), where 1 Hz = 1 cycle per second.

Worked Example

A pendulum completes 5 full swings in 10 seconds.

• Frequency: $f = \dfrac{5 \text{ cycles}}{10\text{ s}} = 0.5\text{ Hz}$
• Period: $T = \dfrac{1}{f} = \dfrac{1}{0.5} = 2\text{ s}$

Check: in 2 seconds you get one cycle, so in 10 seconds you get 5 cycles — consistent.

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