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Alessandra Cummings

Answered question

2022-10-17

What is the period of

f (t) = \sin (4 t) + \cos (24 t)

?

Answer & Explanation

exalantaswo

Beginner2022-10-18Added 14 answers

The period of both

\sin k t

and

\cos k t

is

\frac{2 π}{k}

. So,
the period

P_{1}

of

\cos 24 t

is

\frac{π}{12}

and
the period

P_{2}

of

\sin 4 t = \frac{π}{2} = 6 P_{1}

. And so,
the period of the compounded oscillation

f (t) = \sin 4 t + \cos 24 t

,

P = P_{2} = \frac{π}{2} = 6 P_{1}

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