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The equation of motion of a particle is ...

The equation of motion of a particle is `x=a " cos"(alpha t)^(2)`. The motion is

A

periodic but not simple oscillatory

B

periodic and oscillatory

C

oscillatory but not periodic

D

Neither periodic nor oscillatory

Text Solution

Verified by Experts

The correct Answer is:
C
(c) As the given equation is
`x=a"cos"(alpha t)^(2)`
is a cosine function.Hence , it is an oscillatory motion.
Now, putting t+T in place of t
`x(t+T)=a"cos"[alpha(t+T)]^(2) " "[because x(t)=a"cos"(alphat)^(2)]`
`=a"cos"[alphat^(2)+alphaT^(2)+2alphatT]ne x(t)`
where, T is supposed as period of the function `omega(t)`.
Hence, it is not periodic.
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