Define the frequency of oscillation.

The frequency of oscillation is the number of complete cycles per unit time.

In simple terms, the frequency of oscillation refers to the number of complete cycles that a system undergoes in a given unit of time. It is usually measured in Hertz (Hz), which is defined as the number of cycles per second. For example, if a pendulum completes 10 cycles in 1 second, its frequency of oscillation is 10 Hz.

The frequency of oscillation is determined by the properties of the system undergoing oscillation. For example, the frequency of a simple pendulum is determined by its length and the acceleration due to gravity. The formula for the frequency of a simple pendulum is:

f = 1/(2π) √(g/l)

where f is the frequency, g is the acceleration due to gravity, and l is the length of the pendulum.

In general, the frequency of oscillation can be calculated using the formula:

f = 1/T

where f is the frequency and T is the period of oscillation. The period is the time taken for one complete cycle of oscillation. For example, if a system completes one cycle in 0.5 seconds, its frequency of oscillation is:

f = 1/0.5 = 2 Hz

In summary, the frequency of oscillation is a fundamental property of any system undergoing oscillation, and it is determined by the system's properties such as length, mass, and stiffness. It is measured in Hertz and can be calculated using the formula f = 1/T.