Final answer:
The total energy of a spring oscillator is proportional to the square of the amplitude. If the amplitude doubles while other factors remain constant, the total energy of the oscillator will become four times greater.
Step-by-step explanation:
When discussing the energy of a spring oscillator in the context of physics, the total energy of the system is proportional to the square of the amplitude when all other factors are held constant.
The relevant formula for the potential energy stored in a spring is given by U = ½ k A^2, where U is the potential energy, k is the spring constant, and A is the amplitude.
If the amplitude is doubled, the new energy will be U' = ½ k (2A)^2 = 4 (½ k A^2), which is four times the original energy. Therefore, if the amplitude of a spring oscillator is doubled, the total energy will be quadrupled.