What is the period of f(t)=sin((t)/4)+cos((t)/12)

garkochenvz

garkochenvz

Answered question

2022-08-12

What is the period of f ( t ) = sin ( t 4 ) + cos ( t 12 )?

Answer & Explanation

stangeix

stangeix

Beginner2022-08-13Added 10 answers

The period of both sin kt and cos kt is 2 π k
For the separate oscillations given by sin ( t 4 ) and cos ( t 12 ), the periods are 8 π and 24 π , respectively.
So. for the compounded oscillation given by sin ( t 4 ) + cos ( t 12 ), the period is the L C M = 24 π
In general, if the separate periods are P 1 and P 2 , the period for the compounded oscillation is from m P 1 = n P 2 , for the least positive-integer pair [m, n].
Here, P 1 = 8 π and P 2 = 24 π . So, m=3 and n=1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?