What's the relationship between frequency and period in SHM?

In simple harmonic motion (SHM), the frequency and period are inversely proportional to each other.

In the context of simple harmonic motion, frequency and period are two fundamental concepts that are closely related. The frequency of an oscillation is the number of complete cycles that occur in a given unit of time, typically measured in hertz (Hz), which is equivalent to cycles per second. On the other hand, the period of an oscillation is the time taken for one complete cycle of the motion, usually measured in seconds.

The relationship between frequency (f) and period (T) is given by the equation f = 1/T. This means that as the frequency of the oscillation increases, the period decreases, and vice versa. This inverse relationship is a fundamental characteristic of all oscillatory systems, not just those exhibiting simple harmonic motion.

To understand this relationship intuitively, consider a pendulum swinging back and forth. If the pendulum swings very quickly, completing many swings in a short amount of time, we would say it has a high frequency and a short period. Conversely, if the pendulum swings slowly, taking a long time to complete each swing, it has a low frequency and a long period.

In the context of simple harmonic motion, this relationship between frequency and period becomes particularly important. In SHM, the motion is sinusoidal, meaning it follows a smooth, repeating pattern that can be described mathematically by a sine or cosine function. The frequency and period of the motion directly affect the shape of this sinusoidal pattern. A high frequency (and therefore short period) results in a tightly packed sine wave, with many oscillations occurring in a short span of time. Conversely, a low frequency (and therefore long period) results in a more spread out sine wave, with fewer oscillations occurring over the same span of time.

In conclusion, understanding the relationship between frequency and period is crucial for understanding the behaviour of systems exhibiting simple harmonic motion. This inverse relationship is a fundamental characteristic of all oscillatory systems and is key to describing and predicting their behaviour.