Question

There are 3 combined motions as listed below. (1) Please answer whether these combined motions are periodic or not. If yes, what is the period of the combined motion? (2) Please also answer whether they produce the phenomenon of beats or not. If yes, what is the beat frequency? (a) sin(3t-0.5)+ cos(3t) (b) sin(5t)+cos(5.5t) (c) sin(3t)+cos(t)

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Answer #1

period of sin (at)=2pi/a

period of cos (at)=2pi/a

(a) yes ,it is periodic

period=2pi/3

(b) period of sin (5t)=2pi/5=22pi/55

period of cos (5.5t)=2pi/5.5=4pi/55

period of total=44pi/55

(c)it is non periodic as commom lcm is not possible for 2pi/3 and 2

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