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A particle executing SHM has a maximum s...

A particle executing SHM has a maximum speed of `30 cm//s` and a maximum acceleration of `60 cm/s^(2)` . The period of oscillation is

A

`pi` sec

B

`pi//2` sec

C

`2pi` sec

D

`pi//t` sec

Text Solution

Verified by Experts

The correct Answer is:
A
Let equation of an SHM is represented by `y=asin omegat`.
`v=(dy)/(dt)=a omega cos omegat`
`implies (v)_(max)=a omega=30` . . . (i)
Acceleration `(A)=(dx^(2))/(dt^(2))=-a omega^(2) sin omegat`
`A_(max)=omega^(2)a=60` . . . (ii)
Eqs. (i) and (ii), we get `omega(omega a)=60 implies omega(30)=60`
`implies omega=2 rad//s implies (2pi)/(T)=2rad//s implies T=pi` sec.
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