The mechanical energy of an ideal mass-spring oscillating system starts at 100 joules for a given amplitude. Determine the new mechanical energy of the system.

1) Amplitude is cut in half - Energy?
2) Amplitude is increased by 30% - Energy?
3) Amplitude is decreased by 30% - Energy?

Question

The mechanical energy of an ideal mass-spring oscillating system starts at 100 joules for a given amplitude. Determine the new mechanical energy of the system.

1) Amplitude is cut in half -> Energy?
2) Amplitude is increased by 30% -> Energy?
3) Amplitude is decreased by 30% -> Energy?

anonymous · Answer

I know that energy is proportional to amplitude^2.

anonymous · Answer

imagine that the amplitude starts out at 1. if the energy is proportional to amplitude squared, 1^2=1.
If you halve the amplitude, the new amplitude will be 1/2. How does 1/2^2 compare to 1? If you increase the amplitude by 30%, the amplitude would be 1.3. How does 1.3^2 compare?