Hanging from a horizontal beam are nine simple pendulums of the following length

Question

Hanging from a horizontal beam are nine simple pendulums of the following lengths: (a) 0.50, (b) 1.1, (c) 2.5, (d) 3.1, (e) 3.6, (f) 5.5, (g) 6.5, (h) 0.090, and (i) 0.29 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?




(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Hanging from a horizontal beam are nine simple pendulums of the following lengths: (a) 0.50, (b) 1.1, (c) 2.5, (d) 3.1, (e) 3.6, (f) 5.5, (g) 6.5, (h) 0.090, and (i) 0.29 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?




(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Hanging from a horizontal beam are nine simple pendulums of the following lengths: (a) 0.50, (b) 1.1, (c) 2.5, (d) 3.1, (e) 3.6, (f) 5.5, (g) 6.5, (h) 0.090, and (i) 0.29 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?




(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)

Explanation / Answer

we will get "resonance" when the applied frequency is equal to the natural frequency of a pendulum.

= 2rad/s corresponds to L = g / ² = 9.8m/s² / (2/s)² = 2.45 m
= 4rad/s corresponds to L = 9.8m/s² / (4/s)² = 0.61 m

So the pendulum with a length in this range will resonate at some point for the given applied frequency range. .

From the given choice the only correct answer is  (b) 1.1

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