Calculating Total Energy in Simple Harmonic Motion

[Lavace]

Homework Statement

Calculate the total energy of a 2kg mass that is undergoing simple harmonic motion with an amplitude of 1cm and and frequency of 16Hz.

Homework Equations

ma = -w^{^2}x

The Attempt at a Solution

The first thing I thought was using the general solution of x(t) = A cos(wt + psi), differentiating to find the velocity (after the phase angle, or is this even needed?), and then using the value in K.E = 1/2mv^2?

Please help!

 

[JaWiB]

That might work, but you also need to calculate the potential energy stored in the spring. You may already know the formula or you can find it by integrating the spring force over displacement (work done by the spring is minus the potential energy stored in the spring)

 

[CanIExplore]

The equation you've written

ma = -w^2x

should read a=-w²x right?

ma=-kx
a=-(k/m)x
a=-w²x
where w²=(k/m)

Following JaWiB, potential energy is equal to the negative line integral of the force. U=-$$\int F dl$$, which will come out to a familiar equation you've probably seen before. Since you're given the maximum displacement (amplitude), consider the energy of the particle at its maximum displacement and at the point of equilibrium (x=0). At what points is the energy of the particle purely kinetic or purely potential? Then consider conservation of energy.

 

[Redbelly98]

No integrals are needed here. The OP was right on track:

The Attempt at a Solution

The first thing I thought was using the general solution of x(t) = A cos(wt + psi), differentiating to find the velocity (after the phase angle, or is this even needed?), and then using the value in K.E = 1/2mv^2?

Don't worry about the phase angle, you may assume it's zero for simplicity.
The tricky part is what to do about the potential energy. At some point (value of x) the potential energy is zero, which simplifies the calculation of total energy.