Total mechanical energy of oscillating system?

So I know that the total mechanical energy is E=0.5m*v^2+ 0.5* k*x^2

But sometime I see it written as E=0.5m*v^2+ 0.5* k*A^2

What is the difference?

Here is a question If the amplitutide of the oscillations is doubled the mechanical energy of the system:

Doubles Does not change Other answer :

MY ANSWER does not change. is this correct?

The sum of potential and kinetic energies is constant. The maximum kinetic energy equals the maximum potential energy. So what does this tell you if the amplitude is doubled?

TSny
Homework Helper
Gold Member
So I know that the total mechanical energy is E=0.5m*v^2+ 0.5* k*x^2

But sometime I see it written as E=0.5m*v^2+ 0.5* k*A^2

The second equation is confusing. It is only correct if v represents the speed at the instant x = A. But, what is the speed when x = A? Once you decide, then substitute that value of v into the equation and see what this formula for E simplifies to. (It's the same result as your first equation would give if you let x = A.) That should help you see how E depends on A.

Then the mechanical energy quarduplets :D

TSny
Homework Helper
Gold Member