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