First slide

Applications of SHM

Question

Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is 7 : 8, then the ratio of lengths of the two pendulums will be

Moderate

A

7 : 8
B

8 : 7
C

49 : 64
D

64 : 49

Solution

Suppose at $t = 0$ , pendulums begins to swing simultaneously.
Hence, they will again swing simultaneously
if $n_{1} T_{1} = n_{2} T_{2}$
$⇒ \frac{n_{1}}{n_{2}} = \frac{T_{2}}{T_{1}} = \sqrt{\frac{l_{2}}{l_{1}}} \Rightarrow \frac{l_{1}}{l_{2}} = {(\frac{n_{2}}{n_{1}})}^{2} = {(\frac{8}{7})}^{2} = \frac{64}{49}$

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