Question #173717
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
1
Expert's answer
2021-03-21T11:21:19-0400

Given,

Length of the thread (l1)=10cm=0.1m(l_1)=10cm =0.1m

(l2)=20cm=0.2m(l_2)=20cm= 0.2m

(l3)=30cm=0.3m(l_3)=30cm=0.3m

f=12πglf=\frac{1}{2\pi}\sqrt{\frac{g}{l}}

Now, substituting the values,

f1=12π100.1=102π\Rightarrow f_1=\frac{1}{2\pi}\sqrt{\frac{10}{0.1}}=\frac{10}{2\pi} Hz

f2=12π100.2=502π\Rightarrow f_2=\frac{1}{2\pi}\sqrt{\frac{10}{0.2}}=\frac{\sqrt{50}}{2\pi} Hz

f3=12π100.3=53π\Rightarrow f_3=\frac{1}{2\pi}\sqrt{\frac{10}{0.3}}=\frac{5}{\sqrt{3}\pi}


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