Question

We have a horizontal spring with a mass attached oscillating with a maximum displacement of

A

on either side. At which intermediate displacement(s) the kinetic energy would equal the potential

energy [10]?

Answer 1

Explanations & Calculations

• The point is, the total energy the system has which is the maximum potential energy is equal to the sum of both potential and kinetic energies at a given instance.
• Say the elastic constant is $\small k$ , then

$\qquad\qquad \begin{aligned} \small E_{max}&=\small \frac{1}{2}kA^2\\ \\ \small P.E+K.E&=\small E_m\\ \small P.E+P.E&=\small E_m\cdots\cdots(as\,P.E=K.E)\\ \small 2\Big(\frac{1}{2}kx^2\Big)&=\small \frac{1}{2}kA^2\\ \small x&=\small \frac{A}{\sqrt2} \end{aligned}$