AIEEE 2004 Physics Solved Paper

Given that, initial angular velocity =ω0
and at any instant time t, angular velocity =ω
So when displacement is x then the resultant acceleration
f=(ω02−ω2)x
So the external force, F=m(ω02−ω2)x....(1)
But given that F∝cos‌ω‌t

From (i) we get,
m(ω02−ω2)x∝cos‌ω‌t....(ii)
From equation of SHM we know,
x=Asin‌(ωt+φ)
When t=0 then x=A
∴A=Asin‌(φ)
⇒A=‌

π

2

∴x=Asin‌(ωt+‌

π

2

)=A‌cos‌ω‌t
Putting value of x in (ii), we get
‌m(ω02−ω2)A‌cos‌ω‌t∝cos‌ω‌t
‌⇒A∝‌

1

m(ω02−ω2)