General wave solution:

$\overline{){\mathbf{x}}{\mathbf{=}}{\mathbf{A}}{\mathbf{}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{}}{\mathbf{\left(}}{\mathbf{\omega}}{\mathbf{t}}{\mathbf{\right)}}}$

Potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}}$

The total mechanical energy of the particle:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{K}}{\mathbf{E}}{\mathbf{+}}{\mathbf{U}}}$

Total energy, E, of the system is equal to maximum potential energy, U_{max} = (1/2)kA^{2}.

The motion of a particle is given by *x*(*t*)=(25cm)cos(15*t*), where *t* is in s.

What is the first time at which the kinetic energy is twice the potential energy?

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