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**1. Homework Statement**

A particle with a mass of 0.500 kg is attatched to a spring with a force constant of 50.0 N/m. At time t = 0 the particle has its maximum speed of 20.0 m/s and is moving to the left. (Use t as necessary.)

(a) Determine the particle's equation of motion, specifying its position as a function of t, time.

(b) Where in the motion is the potential energy three times the kinetic energy?

(c) Find the length of a simple pendulum with the same period.

(d) Find the minimum time interval required for the particle to move from x = 0 to x = 1.00 m.

**3. The Attempt at a Solution**

I only need help with the first part for now, but here is what I tried.

[tex]\omega = \sqrt{\frac{k}{m}}[/tex]

[tex]\omega = 10[/tex]

[tex]v_{max} = A\omega[/tex]

[tex]A = 2[/tex]

So my equation of motion looked like this.

[tex]x(t) = 2cos(10t)[/tex]

but that was wrong and I am not entirely sure why