Energy in Oscillation Video Lessons

Concept

# 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.

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###### 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?