Physics aplitude problem... need answer asap...?

Question

If a vibrating system has total energy E_0, what will its total energy be (in terms of E_0) if you double the amplitude of vibration?

If you want to triple the total energy of a vibrating system with amplitude A_0, what should its new amplitude be (in terms of A_0)?

Answer 1

The total energy of the system is

1/2 k A^2

If you double the amplitude, you quadruple the energy.

To triple the energy of the system, solve

1/2 k x^2 = ( 3 ) 1/2 k A^2

for x. You'll get the answer in terms of A, as desired.