A mass is oscillating with amplitude A at the end of a spring.?

Question

How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?

I understand your answer but i am struggling with the algebra aspect of this problem. I had the same thing but i can not get the correct answer for whatever reason

Answer 1

The total energy of the system when the spring when fully extended is

1/2 k A^2

You want to know the displacement where potential energy = kinetic energy. Another way to say that is, you want the position where the potential energy is half of the maximum. In other words, you want to solve

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

for x. The answer will be in terms of A, as desired.

Answer 2

d = .707