(a) `KE = 0` `PE = 1/2kA^2` (b) `KE = 1/2mv^2` `PE = 0` (c) `KE = 0` `PE = 1/2kA^2` (d) `KE = 1/2mv^2` `PE = 1/2kx^2`
The total mechanical energy of a simple harmonic oscillator is proportional to the square of the amplitude. `1/2mv^2+1/2kx^2 = 1/2kA^2` `v^2 = (k(A^2-x^2))/m` `v^2 = k/mA^2(1-x^2/A^2)` Since `1/2mv_(max)^2 = 1/2kA^2` we get `v_(max)^2 = (k/m)A^2` `v^2 = v_(max)^2(1-x^2/A^2)`