Question

What is the period of `f(t)=sin( t /2 )+ cos( (13t)/24 )`?

Answer 1

`52pi`

Explanation:

The period of both sin kt and cos kt is `(2pi)/k`.

So, separately, the periods of the two terms in f(t) are `4pi and (48/13)pi`.

For the sum, the compounded period is given by `L(4pi)=M((48/13)pi)`, making the common value as the least integer multiple of `pi`.

L=13 and M=1. The common value = `52pi`;

Check: `f(t+52pi)=sin ((1/2)(t+52pi))+cos ((24/13)(t+52pi))`
`=sin(26pi+t/2)+cos(96pi+(24/13)t)`
`=sin(t/2)+cos(24/13t)=f(t)`..