Frequency of combined motion

In summary, the frequency of the combined motion of (b)sin(12\pi t )+cos(13\pi t-\frac{\pi}{4}) is 6.25 or 25/4, and for (c)sin(3t)-cos(\pi t), it is 0.49 Hz. The attempt at a solution involved finding the values of \omega and T for each function and trying to combine them, but ultimately it was incorrect.
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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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no need to answer i found this same question in another thread. just don't know how to delete
 

1. What is combined motion?

Combined motion refers to the movement or displacement of an object or body in multiple directions or along multiple paths simultaneously.

2. How is frequency related to combined motion?

Frequency is the number of complete cycles of motion that an object undergoes in a given time period. In the case of combined motion, the frequency is determined by the individual frequencies of each component motion.

3. Can frequency of combined motion be calculated?

Yes, the frequency of combined motion can be calculated by adding the individual frequencies of each component motion. For example, if an object is moving with a frequency of 10 Hz in the x-direction and 5 Hz in the y-direction, the frequency of the combined motion would be 15 Hz.

4. How does the amplitude of each component motion affect the frequency of combined motion?

The amplitude of each component motion does not affect the frequency of combined motion. The frequency is solely determined by the individual frequencies of each component motion.

5. What are some real-life examples of combined motion?

Some examples of combined motion in real life include a pendulum swinging back and forth while also rotating in a circular motion, a car driving in a curved path while also vibrating due to a bumpy road, and a satellite orbiting the Earth while also rotating on its own axis.

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