What Is the Frequency of Combined Motion?

[bfusco]

Homework Statement

This is for review, i have a test coming up.

Find the frequency of the combined motion of each of the following:
(b)sin(12\pi t )+cos(13\pi t-\frac{\pi}{4})
(c)sin(3t)-cos(\pi t)

The Attempt at a Solution

(b)\omega_1 =12\pi, \omega_2 =13\pi

T=\frac{2\pi}{\omega}, so

T_1 = \frac{2\pi}{12\pi} = 1/6

T_2 = \frac{2\pi}{13\pi} = 2/13

T=n_1 T_1 = n_2 T_2 → T=n_1 * 1/6=n_2 * 2/13

n_1 = 12 n_2 = 13

T=2 → f=1/2

Apparently the answer is f=6.25 or 25/4

(c) since \omega_1 = 3 and \omega_2 = \pi

T_1 =\frac{2\pi}{3} T_2 = \frac{2\pi}{\pi} = 2

since \pi is irrational there is no integer i can multiply T_2 by in order to have it match T_1 so i assumed they cannot be combined, but again that is incorrect. apparently the answer is f=.49 Hz.

Any help is appreciated, thank you.

 

[bfusco]

no need to answer i found this same question in another thread. just don't know how to delete