AIIMS 2017 Physics Question Paper for free online practice with solutions

The displacement of a particle in S.H.M. is given by
y=a sin(ωt+ϕ)
velocity=

dy

dt

=ωa cos(ωt+ϕ)
The velocity is maximum when the particle passes through the mean position i.e.,
(

dy

dt

)max=ωa
The kinetic energy at this instant is given by

1

2

m(

dy

dt

)max2=

1

2

mω2a2 =8×10−3 joule
or

1

2

×(0.1)ω2×(0.1)2=8×10−3
Solving we get ω±4
Substituting the values a,ω and ϕ in the equation of S.H.M.,we get
y=0.1 sin(±4t+

π

4

)metre.