the ratio of kinetic energy of the particle at mean position to the point where distance is half of the amplitude will be
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Explanation:
Particle's position x=
2
A
Velocity of particle at that position v=w
A
2
−x
2
∴ v=w
A
2
−(A/2)
2
=
2
3
Aw
Kinetic energy K=
2
1
mv
2
=
2
1
m×
4
3
A
2
w
2
⟹ K=
2
1
k.
4
3
A
2
(∵k=mw
2
)
Potential energy U=
2
1
kx
2
=
2
1
k.
4
A
2
∴ Ratio
U
K
=
2
1
k.
4
A
2
2
1
k.
4
3
A
2
=3
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