My question had 2 parts:

a) A 2.0 kg object oscillates with simple harmonic motion on a spring of force constant 580.0 N/m. The maximum speed is 1.0 m/s. What is the total energy of the object and the spring?
Answer: 1.0 J

b) What is the maximum amplitude of the oscillation?
This question seems like it would be easy, but I just don't understand what I'm solving for.

N/m. I was doing it right all along, but the computer wasn't accepting meters as the correct unit.

To solve part a) of your question and find the total energy of the object and the spring, you can use the equation for the total mechanical energy of a simple harmonic oscillator:

E = (1/2)kA^2

where E is the total mechanical energy, k is the force constant of the spring, and A is the amplitude of the oscillation.

In this case, you are given the force constant of the spring (k = 580.0 N/m), so we need to find the amplitude (A) of the oscillation.

To solve part b) of your question and find the maximum amplitude of the oscillation, we can use the equation for the maximum speed (v_max) of a simple harmonic oscillator:

v_max = ωA

where v_max is the maximum speed, ω is the angular frequency, and A is the amplitude.

In this case, you are given the maximum speed of the object (v_max = 1.0 m/s), so we need to find the angular frequency (ω) and then we can solve for the amplitude (A).

To find the angular frequency (ω), we can use the equation:

ω = sqrt(k/m)

where ω is the angular frequency, k is the force constant of the spring, and m is the mass of the object.

In this case, you are given the mass of the object (m = 2.0 kg) and the force constant of the spring (k = 580.0 N/m), so you can plug these values into the equation to find ω.

Once you have found ω, you can use the equation v_max = ωA to solve for A, the maximum amplitude of the oscillation.

By finding the amplitude (A), you can substitute this value back into the equation for the total mechanical energy (E = (1/2)kA^2) to get the answer for part a) of your question.