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Out of the following functions represent...

Out of the following functions representing motion of a particle which represents SHM
I. `y = sin omega t - cos omega t`
II. `y = sin^(3)omega t`
III. `y = 5 cos ((3 pi)/(4)-3 omega t)`
IV. `y = 1 + omega t + omega^(2)t^(2)`

A

Only 1

B

Only 4 does not represent SHM

C

Only 1 and 3

D

Only 1 and 2

Text Solution

Verified by Experts

The correct Answer is:
C
(1) `y=sinomegat-cosomegat`
`=sqrt(2)[(1)/(sqrt(2))sinomegat-(1)/(sqrt(2))cosomegat]`
(2) `y=sin^(3)omegat`
`=(1)/(4)[3sinomegat-sin3omegat]`
This is periodic motion with 2 different frequency
(3) `y=5cos((3pi)/(4)-3omegat)`
`=5cos(3omegat-(3pi)/(4))(because cos(-theta)=costheta)`
It is S.H.M. with time period `T=(2pi)/(3omega)`
(4) `y=1+omegat+omega^(2)t^(2)`
It is non-periodic motion y will increase monotonously with time So, (1) and (3) represents S.H.M.
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