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## 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)[itex]sin(12\pi t )+cos(13\pi t-\frac{\pi}{4})[/itex]

(c)[itex]sin(3t)-cos(\pi t) [/itex]

## The Attempt at a Solution

(b)[itex]\omega_1 =12\pi [/itex], [itex]\omega_2 =13\pi [/itex]

[itex]T=\frac{2\pi}{\omega} [/itex], so

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

[itex] T_2 = \frac{2\pi}{13\pi} = 2/13[/itex]

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

[itex]n_1 = 12[/itex] [itex]n_2 = 13[/itex]

T=2 → f=1/2

Apparently the answer is f=6.25 or 25/4

(c) since [itex]\omega_1 = 3 [/itex] and [itex]\omega_2 = \pi [/itex]

[itex]T_1 =\frac{2\pi}{3} [/itex] [itex]T_2 = \frac{2\pi}{\pi} = 2[/itex]

since [itex]\pi[/itex] is irrational there is no integer i can multiply [itex]T_2[/itex] by in order to have it match [itex]T_1[/itex] 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.

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