What is the relationship between period and frequency in simple harmonic motion?

The period and frequency in simple harmonic motion are inversely proportional.

In simple harmonic motion, an object moves back and forth in a periodic motion. The period is the time taken for one complete oscillation, while the frequency is the number of oscillations per second. The relationship between the two is that they are inversely proportional. This means that as the period increases, the frequency decreases, and vice versa.

Mathematically, the relationship can be expressed as T = 1/f, where T is the period and f is the frequency. This equation shows that if the frequency is doubled, the period is halved, and if the frequency is halved, the period is doubled.

The relationship between period and frequency is important in understanding simple harmonic motion. For example, if the period of a pendulum is known, the frequency can be calculated using the equation f = 1/T. Similarly, if the frequency of a sound wave is known, the period can be calculated using the same equation.

In conclusion, the period and frequency in simple harmonic motion are inversely proportional. Understanding this relationship is important in many areas of physics, including mechanics and waves.