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Introductory Physics Homework Help
Frequency of combined motion
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[QUOTE="bfusco, post: 4511037, member: 400372"] [h2]Homework Statement [/h2] 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][h2]The Attempt at a Solution[/h2] (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. [/QUOTE]
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Frequency of combined motion
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