KEAM 2019 Physics and Chemistry Paper

Let displacement equation of a particle executing SHM is given as
x=a‌sin‌ω‌t
then velocity (v)=‌

dx

dt

=aω‌cos‌ω‌t .....(i)
and acceleration (a)=‌

d2x

dt2

=‌

dv

dt

=−aω2‌sin‌ω‌t
a=aω2‌cos(ωt+‌

π

2

)....(ii)
(∵cos(θ+‌

π

2

)=−sin‌θ)
Now, comparing Eqs (i) and (ii), we can conclude that the acceleration lead the velocity by a phase of +‌

π

2

radians.