What is the period of the sinusoid s(t)=Asin(2πf0t)

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To find the period of the sinusoid s(t) = A * sin(2πf0t), we need to understand the equation of a sinusoid.

A sinusoid is a mathematical function that represents a repetitive oscillation or wave-like pattern. It is characterized by its amplitude (A), frequency (f0), and phase (Φ).

The period of a sinusoid is the time it takes for one complete cycle of the waveform. In other words, it indicates the length of time required to repeat the pattern.

In the equation s(t) = A * sin(2πf0t), the variable t represents time. The term 2πf0t in the equation determines the position of the waveform at any given time t.

To find the period, we need to determine the value of t for which the sinusoid completes one full cycle. This can be done by finding the time when the angle of the sine function reaches a full revolution (360 degrees or 2π radians).

Since the argument of the sine function is 2πf0t, we can set it equal to 2π and solve for t:

2πf0t = 2π

Dividing both sides of the equation by 2πf0, we get:

t = 1 / f0

Therefore, the period (T) of the sinusoid is the reciprocal of the frequency (f0):

T = 1 / f0

So, to find the period of the sinusoid s(t) = Asin(2πf0t), you can calculate the reciprocal of the frequency f0.