Initially, an object in simple harmonic motion with an amplitude A and a period

Question

Initially, an object in simple harmonic motion with an amplitude A and a period T. Then, without changing its period (or the mass of the object), the amplitude is doubled to 2A. How has the energy of the system containing this object changed?

It was reduced to half its initial value.

It has gone up by a factor of 4.

It has doubled.

It is now 16 times its previous value.

It has increased by a factor of 8.

a)

It was reduced to half its initial value.

b)

It has gone up by a factor of 4.

c)

It has doubled.

d)

It is now 16 times its previous value.

e)

It has increased by a factor of 8.

Explanation / Answer

Initial energy

E1= 0.5*kA^2

Final energy in system

E2= 0.5* k (2A)^2

E2= 4*(0.5kA^2)

E2= 4* E1

It has gone up by factor 4.

Option (b) is correct.

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Comment in case any doubt..goodluck

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