Question

An object in simple harmonic motion has an amplitude of $4.0cm$, a frequency of $2.0Hz,$and a phase constant of $2\mathrm{\pi }/3rad.$Draw a position graph showing two cycles of the motion.

Short answer

position graph as follow

Step-by-step solution

Given information

amplitude $a=4.0cm$

frequency $f=2.0Hz$

phase constant$\theta =\frac{2\mathrm{\pi }}{3}rad$

Explanation

The wave equation is in the form

$x=a\cos \left(\omega t+\theta \right)$

The angular frequency is in the form

$\omega =2\mathrm{\pi f}=4\mathrm{\pi }rad/s$

The equation now takes the form of substituting the values of angular frequency and phase constant.

$x=(4.0cm)\cos \left(4\mathrm{\pi }t+\frac{2\mathrm{\pi }}{3}\right)$

Therefore the position graph shows two cycles of motion are as follows.