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The equation of motion of a particle is ...

The equation of motion of a particle is `x=acos(alphat)^(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
As the given equation is
`x=acos(alphat)^2`
is a cosine fucntion. Hence, it is an oscillatory motion.
Now, putting `t+T` in place of t
`x(t+T)=acos[alpha(t+T)]^(2)" "[because x(t)=acos(alphat)^2]`
`=acos [alpha^(2)t^(2)+alpha^(2)T^(2)+2alpha^(2)tT]ne x(t)`
where, T is supposed as period of the function `omega (t)`. Hence, it is not periodic.
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