Question

The energy of a system in simple harmonic motion is given by E=½m⍵²A². Which of the two statements is more appropriate?
(A) The energy is increased because the amplitude is increased.
(B) The amplitude is increased because the energy is increased.

Answer 1

Since, Total Energy for any Simple Harmonic Motion is constant. It depends only on the Amplitude of the S.H.M.

Total energy = 1/2kA²= 1/2 m⍵²A²

Now, For the given mass, if the Energy will be large then the Amplitude of the S.H.M. is large.

Now, Both statement given in the question are correct but second statement is more correct because if energy is increased then only the amplitude can increase.

Amplitude cannot increase by itself, some external work must be done to increase it.

Thus second statement in  more appropriate.  Although both are correct.

Hoe it helps.