A mass attached to a very light spring executes simple harmonic motion. If you want to double its total energy, you should

Question

BlackTom AI · Accepted Answer

This problem deals with the energy in a mass-spring system performing simple harmonic motion. The total mechanical energy in SHM can be written in a couple of ways: E = (1/2) k A^2 and E = (1/2) m v_max^2, with v_max = A sqrt(k/m).

Option: 'double the force constant of the spring while changing nothing else.' If you increase the spring constant k to 2k while keeping the mass m and amplitude A the same, the energy expression E = (1/2) k A^2 becomes E' = (1/2) (2k) A^2 = 2 × (1/2) k A^2, i.e., the total energy doubles.

To consider why the other possibilities (if they were present) might not apply: increasing amplitude A by a factor of sqrt(2) with the same k would also double the energy, since E ∝ A^2. Conversely, changing other parameters without affecting the combination that sets E ≈ (1/2) k A^2 would not necessarily double E.

In summary, given the option presented, doubling the spring constant while keeping all else unchanged will indeed double the total energy of the mass-spring system in SHM.

SPHY001 Practice Quiz - Unit 16 | LA056

A mass attached to a very light spring executes simple harmonic motion. If you want to double its total energy, you should

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