To solve this problem, we must consider the properties of a Simple Harmonic Motion (SHM) system. The total mechanical energy, potential energy, and kinetic energy are all linked to the amplitude of the motion.
The total energy \(E\) of a system undergoing SHM is given by the formula:
\(E = \frac{1}{2}kA^2\),
where \(k\) is the spring constant and \(A\) is the amplitude. Doubling the amplitude implies that the energy, based on the square of the amplitude, becomes four times, not twice.
The maximum kinetic energy \(K_{\text{max}}\) at the equilibrium position is equal to the total energy:
\(K_{\text{max}} = \frac{1}{2}kA^2\).
If the amplitude doubles, maximum kinetic energy is affected similarly to total energy, increasing four times.
The maximum potential energy \(U_{\text{max}}\) at the extreme displacement is also:
\(U_{\text{max}} = \frac{1}{2}kA^2\).
This behaves the same way as total energy—quadrupled with doubled amplitude.
The maximum velocity \(v_{\text{max}}\) is given by:
\(v_{\text{max}} = A\omega\),
where \(\omega = \sqrt{\frac{k}{m}}\) is the angular frequency, which is independent of amplitude. Doubling the amplitude results in the doubling of maximum velocity.
From the reasoning above, the conclusion is that when the amplitude of a body executing SHM becomes twice, the correct answer is:
Maximum velocity is doubled.
This confirms the given correct answer.