Question

A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. At what location are the kinetic energy and the potential energy the same

Answer 1

Given :

A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface.

The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position.

To Find :

At what location are the kinetic energy and the potential energy the same.

Solution :

Let, at location x from the equilibrium position the kinetic energy and the potential energy the same.

So,

`P.E = K.E\\\\(kx^2)/(2) = (mv^2)/(2)\\\\x = v\sqrt{(m)/(k)}\\\\x = 1.5 * \sqrt{(0.5)/(20)}\ m\\\\x = 0.238 \ m`

Hence, this is the required solution.