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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` s

B

`(pi)/(2)` s

C

`2pi` s

D

`(pi)/(t)` s

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Let equation of an SHM is represent by `y=a "sin"omegat`
`v=(dy)/(dt)=a omega " cos" omegat`
`implies (v)_("max")=aomega=30" "…(i)`
Acceleration (A) `=(dy^(2))/(dt^(2))=-aomega^(2)"sin"omegat`
`A_("max")=omega^(2)a=60 " "...(ii)`
Eqs. (i) and (ii) , we get
`omega(omegaa)=60impliesomega(30)=60`
`implies omega=2 "rad"s^(-1)`
`implies(2pi)/(T)=2"rad"s^(-1)`
`impliesT=pis^(-1)`
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