# Problem: The motion of a particle is given by x(t)=(25cm)cos(15t), where t is in s.What is the first time at which the kinetic energy is twice the potential energy?

###### FREE Expert Solution

General wave solution:

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, Umax = (1/2)kA2.

###### Problem Details

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

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

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Energy in Oscillation concept. You can view video lessons to learn Energy in Oscillation. Or if you need more Energy in Oscillation practice, you can also practice Energy in Oscillation practice problems.