Question

Hanging from a horizontal beam are nine simple pendulums ofthe following lengths: (a) 0.10, (b) 0.30, (c) 0.40, (d) 0.80, (e)1.2, (f) 2.8, (g) 3.5, (h) 5.0, and (i) 6.2 m. Suppose the beamundergoes horizontal oscillations with angular frequencies in therange from 2.00 rad/s to 4.00 rad/s. Which of the pendulums will be(strongly) set in motion?

Answer 1

The pendulums that will be strongly set in motion can be determined by comparing their natural frequencies to the range of angular frequencies of the beam. By calculating the natural frequencies using the length of each pendulum, we can identify which ones fall within the given range.

Step-by-step explanation:

In order to determine which pendulums will be strongly set in motion, we need to find the natural frequency of each pendulum and compare it to the range of angular frequencies of the beam. The natural frequency of a simple pendulum is given by the formula:

f = (1/2π) * √(g/L)

where f is the frequency, g is the acceleration due to gravity, and L is the length of the pendulum. By calculating the natural frequencies of each pendulum, we can determine which ones fall within the angular frequency range of the beam.

For example, if we take pendulum (a) with a length of 0.10 m, the natural frequency can be calculated as:

f = (1/2π) * √(9.8/0.10) = 3.13 Hz

Comparing this frequency to the range of angular frequencies (2.00 rad/s to 4.00 rad/s), we can see that pendulum (a) will be strongly set in motion because its natural frequency falls within this range.