Question

The total mechanical energy of a spring-mass system in simple harmonic motion is E = ½m⍵²A². Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same. The new mechanical energy will
(a) become 2E
(b) become E/2
(c) become √2E
(d) remain E.

Answer 1

Energy of the Simple Harmonic Motion is given by the Relation,

 E = 1/2 × m⍵²A²

∴ E = 1/2 × kA²

Now, K is the cosnatnt of the S.H.M.

If the mass of the particle will increase it will have no effect on the Energy. It depends only on the Amplitude of the Motion which can only be increased due to the work which will be done on it.

But in given case, no work is done and hence, the Energy of the S.H.M. will remains the same as that of the E.

Therefore, Option (d). is correct.

Hope it helps.

Answer 2

Answer:

d) remains E

Explanation:

Given,

The total mechanical energy of a spring-mass system in simple harmonic motion is E = ½m⍵²A²

Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude A remains the same

To find: The new mechanical energy

Solution:

E = 1/2m⍵²A²

E = m/2*k/m*A²

E = 1 / 2 kA² ..

We can see that the Energy is independent of the mass .

Therefore, We can can the energy remains E for all values of mass.

Hence, Option d) remains E is correct.