Answer to Question #173717 in Classical Mechanics for Gergana

Question

The ball is hung on a thread with a length of l = 20cm. Three other balls are hung on strings. The length of one thread of the ball is l = 10cm, of the other l = 20cm, and of the third l = 30 cm.
1. Determine the natural frequencies of mathematical pendulums
2. Divert the ball with length l = 20cm from its equilibrium position and let it vibrate freely. the amolitus with which the other balls begin to vibrate. When vibrating, which of the balls does not have a resonance? (g = 10m /s

Answer 1

Given,

Length of the thread $(l_1)=10cm =0.1m$

$(l_2)=20cm= 0.2m$

$(l_3)=30cm=0.3m$

$f=\frac{1}{2\pi}\sqrt{\frac{g}{l}}$

Now, substituting the values,

$\Rightarrow f_1=\frac{1}{2\pi}\sqrt{\frac{10}{0.1}}=\frac{10}{2\pi}$ Hz

$\Rightarrow f_2=\frac{1}{2\pi}\sqrt{\frac{10}{0.2}}=\frac{\sqrt{50}}{2\pi}$ Hz

$\Rightarrow f_3=\frac{1}{2\pi}\sqrt{\frac{10}{0.3}}=\frac{5}{\sqrt{3}\pi}$