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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 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
The equation of motion of a particle is `x= a cos (alpha t)^(2)` is a cosine function hence, motion is oscillatory.
Now putting `t+T` instead of t,
`x(t+T)= a cos [alpha (t+T)^(2)]" "[therefore x(t) = a cos (alpha t)^(2)]`
`=a cos [alpha t^(2) + alphaT^(2) +2 alpha t T] ne x(t)`
where, T is a period of the function `omega (t)`
Hence given motion is oscillatory but not periodic.
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