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Equation of a particle on a spring

A particle with a mass of .500 kg is attached to a spring with a force constant of 50.0 N/m. At time t=0 the particle has its maximum spreed of 20.0 m/s and is moving to the left. (a) Determine the particle's equation of motion, specifying its position as a function of time. (b) Where in the motion is the potential energy three times the kinetic energy? (c) Find the minimum time interval required for the particle to move from x=0 to x=1m.

I'm not sure if I use x(t) = A cos(omegat + phi) I need some guidance. Can you help? I'm having a lot of trouble understanding oscillatory motion.

Solution Summary

This solution is provided in a three page .pdf file. It discusses and explains oscillatory motion and provides equations and calculations for solving the problem.