Question

A simple harmonic oscillator has a mass of 1.4 kg, a maximum speed of 0.55 m/s, and a spring constant of 20.5 N/m. Use Conservation of Energy to find the amplitude of the system. Assume that there are no frictional losses.

Answer 1

Here we have given ,

We have a simple harmonic oscillator

Whose mass =1.4 kg

(Vo) maximum speed = 0.55 m/s,

spring constant k = 20.5 N/m

Using Conservation of Energy to find the amplitude of the system we have a relationship as

Kf+ Uf = Ki+Ui

Where Kf and Ki are final kinetic energy and initial kinetic energy respectively

And Ui and Uf are initially potential and final potential energy

Now on plugging values we will have,

1/2×mV1^2 + 1/2×k×x^2 = 1/2×mVo^2 + 0J

0J + 1/2×k×A^2 = 1/ 2×mvo^2

Here A is the amplitude of the system.

So that ,

A = (m/k)^1/2 ×Vo= 0.143730 m

Hence the amplitude of the system = 0.143730 m