Total mechanical energy of oscillating system?

[Questions999]

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?

 

[LawrenceC]

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]

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.

 

[Questions999]

Then the mechanical energy quarduplets :D

 

[TSny]