Question

what is the displacment of object performing simple harmonic motion when kinetic and potiential energy are equal?

Answer 1

Answer on Question#37874, Physics, Other

Question:

what is the displacement of object performing simple harmonic motion when kinetic and potential energy are equal?

Answer:

Let us consider a harmonic oscillator with total energy which is the sum of kinetic energy $T$ and potential energy $U$:

$$E = T + U$$

or

$$E = \frac{m v^{2}}{2} + \frac{k x^{2}}{2}$$

where $m$ – is a mass of the object, $v$ – its velocity, $x$ – its displacement, $k$ – a coefficient characterizing the system.

If at some moment of time the kinetic energy $T$ is equal to potential energy $U$ then the displacement of the object is

$$x = \sqrt{\frac{m v^{2}}{k}}$$

or

$$x = \sqrt{\frac{2 T}{k}} = \sqrt{\frac{E}{k}}$$