Question

Hanging from a horizontal beam are nine simple pendulums of the following lengths: (a) 2.7, (b) 3.1, (c) 3.8, (d) 5.3, (e) 6.6, (f) 0.060, (g) 0.24, (h) 0.45, and (i) 1.0 m. Suppose the beam undergoes horizontal oscillations with angular frequencies in the range from 2.00 rad/s to 4.00 rad/s. Which of the pendulums will be (strongly) set in motion?

Answer 1

Angular velcoity of a pendulum of length L is given by sqrt(g/L)

angular frequency of the pendulums are:

a)sqrt(9.8/2.7)=1.91 rad/s

b)sqrt(9.8/3.1)=1.78 rad/s

c)sqrt(9.8/3.8)=1.61 rad/s

d)sqrt(9.8/5.3)=1.36 rad/s

e)sqrt(9.8/6.6)=1.22 rad/s

f)sqrt(9.8/0.06)=12.78 rad/s

g)sqrt(9.8/0.24)=6.39 rad/s

h)sqrt(9.8/0.45)=4.67 rad/s

i)sqrt(9.8/1)=3.13 rad/s

Given angular frequency range iun which pendulums are oscillating is 2 - 4 rad/s

Therefore, if the natural angular frequcny of a pendulum lies within the range of 2-4 rad/s or if the multiple of natural angular frequency of pendulum lies within the range 2-4 rad/s, then that pendulum will be stroingly set to motion.

Those pendulums are:

a,b,c,d,e and i