Question

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. `pisec`
B. `(pi)/(2)sec`
C. `2pisec`
D. `(pi)/(t)sec `

Answer 1

Let equation of an SHM is represented by `y=asinomegat`
`v=(dy)/(dt)=aomegacosomegat`
`rArr(v)max=aomega=30`" " .....(i)`
Acceleration `(A)=(dx^(2))/(dt^(2))=-aomega^(2)sinomegat`
`A_(max)=omega^(2)a=60" " .....(ii)`
Eqs. (i) and (ii), we get `omega(omegaa)=60rArromega(30)=60`
`rArromega=2rad//s`
`rArr(2pi)/(T)=2red//srArrT=pisec`