Question

Consider a situation of simple harmonic motion in which the distance between the endpoints is 2.39 m and exactly 8 cycles are completed in 22.7 s. When this motion is viewed as a projection of circular motion, what are the radius, r, and angular velocity, ? , of the circular motion?

Answer 1

1.195 m

2.8375 s

2.21433 rad/s

Step-by-step explanation:

d = Distance = 2.39 m

N = Number of cycles = 8

t = Time to complete 8 cycles = 22.7 s

Radius would be equal to the distance divided by 2

`r=(d)/(2)\\\Rightarrow r=(2.39)/(2)\\\Rightarrow r=1.195\ m`

The radius is 1.195 m

Time period would be given by

`T=(t)/(N)\\\Rightarrow T=(22.7)/(8)\\\Rightarrow T=2.8375\ s`

Time period of the motion is 2.8375 s

Angular speed is given by

`\omega=(2\pi)/(T)\\\Rightarrow \omega=(2\pi)/(2.8375)\\\Rightarrow \omega=2.21433\ rad/s`

The angular speed of the motion is 2.21433 rad/s