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I translated it, so the notation may not be so great.

You have a vertical spring with a spring constant of 16 N.m^-1, we attach to its lower end a body with a mass of 0,4 KG and form a system which oscillates on a straight line with length of 8cm, we assume that at the start of the time, the body is in its equilibrium point and moving in the negative direction (the axis is directed downwards).

1. Find the period for oscillations and the displacement function.

2. Find the velocity and momentum function, calculate them at t = 1/2s. Calculate the kinetic energy at the same time.

I didn't have a problem with the first question, I got T=1s and the function for displacement: x=0.04 cos(2*π*t+π/2) What I'm having problem with is the kinetic energy,

if I calculate it by:

1/2 * m * v^2 I get 125*10^-4

Because v at t = 1/2 is 25*10^-2.

If I calculate it by:

1/2 * k * Xmax^2 I get 128*10^-4

Because at t=1/2, the mechanical energy is all kinetic energy.

What am I doing wrong? Which answer is correct, why is there a small 3 unit difference?

You have a vertical spring with a spring constant of 16 N.m^-1, we attach to its lower end a body with a mass of 0,4 KG and form a system which oscillates on a straight line with length of 8cm, we assume that at the start of the time, the body is in its equilibrium point and moving in the negative direction (the axis is directed downwards).

1. Find the period for oscillations and the displacement function.

2. Find the velocity and momentum function, calculate them at t = 1/2s. Calculate the kinetic energy at the same time.

**2. Homework Equations****3. The Attempt at a Solution**I didn't have a problem with the first question, I got T=1s and the function for displacement: x=0.04 cos(2*π*t+π/2) What I'm having problem with is the kinetic energy,

if I calculate it by:

1/2 * m * v^2 I get 125*10^-4

Because v at t = 1/2 is 25*10^-2.

If I calculate it by:

1/2 * k * Xmax^2 I get 128*10^-4

Because at t=1/2, the mechanical energy is all kinetic energy.

What am I doing wrong? Which answer is correct, why is there a small 3 unit difference?

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