Question

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

Answer 1

`24pi`

Explanation:

The period of both sin kt and cos kt is `(2pi)/k`.
For the separate oscillations given by `sin(t/4) and cos(t/12)`, the periods are `8pi and 24pi`, respectively.

So. for the compounded oscillation given by `sin(t/4)+cos(t/12)`, the period is the LCM = `24pi`.

In general, if the separate periods are `P_1 and P_2`, the period for the compounded oscillation is from `mP_1=nP_2`, for the least positive-integer pair [m, n].

Here, `P_1=8pi and P_2=24pi`. So, m = 3 and n = 1.