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?

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boffeemadrid boffeemadrid · Answer 1 · 2019-12-04T08:36:24+01:00

Answer:

1.195 m

2.8375 s

2.21433 rad/s

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

[tex]r=\frac{d}{2}\\\Rightarrow r=\frac{2.39}{2}\\\Rightarrow r=1.195\ m[/tex]

The radius is 1.195 m

Time period would be given by

[tex]T=\frac{t}{N}\\\Rightarrow T=\frac{22.7}{8}\\\Rightarrow T=2.8375\ s[/tex]

Time period of the motion is 2.8375 s

Angular speed is given by

[tex]\omega=\frac{2\pi}{T}\\\Rightarrow \omega=\frac{2\pi}{2.8375}\\\Rightarrow \omega=2.21433\ rad/s[/tex]

The angular speed of the motion is 2.21433 rad/s