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## Homework Statement:

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## Relevant Equations:

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Consider the following periodic function:

## f(t) = \sin(ωt) + \cos(2ωt) + \sin(4ωt) ##

What is the time period of the above periodic function?

The following is given in my book:

Period is the least interval of time after which the function repeats. Here, ##\sin(ωt)## has a period ##T_o = \frac{2π}{ω}##, ##\cos(2ωt)## has a period ##\frac{T_o}{2}## and ##\sin(4ωt)## has a period of ##\frac{T_o}{4}##. The period of the first term is a multiple of the periods of the last two terms. Therefore, the smallest interval of time after which the sum of the three terms repeats is ##T_o##, and thus, Time period is ##T_o##.

I don't understand what the above lines mean.

## f(t) = \sin(ωt) + \cos(2ωt) + \sin(4ωt) ##

What is the time period of the above periodic function?

The following is given in my book:

Period is the least interval of time after which the function repeats. Here, ##\sin(ωt)## has a period ##T_o = \frac{2π}{ω}##, ##\cos(2ωt)## has a period ##\frac{T_o}{2}## and ##\sin(4ωt)## has a period of ##\frac{T_o}{4}##. The period of the first term is a multiple of the periods of the last two terms. Therefore, the smallest interval of time after which the sum of the three terms repeats is ##T_o##, and thus, Time period is ##T_o##.

I don't understand what the above lines mean.