Question

Simple pendulum whose length is slightly less than that of seconds pendulum starts vibrating with another seconds pendulum after 18 seconds they again vibrate in the same phase. The periodic time is

Answer 1

Answer:

A simple pendulum consists of perfectly flexible in extensible and massless string which is fixed from rigid support from one end and from one end consists of small point mass object called bob.

Answer 2

The periodic time is 1.8 seconds.

Explanation:

It is mentioned that, simple pendulum whose length is slightly less than that of seconds pendulum starts vibrating with another seconds pendulum after 18 seconds they again vibrate in the same phase. Let T = 18 s, the time period of the simple pendulum is 2 s, T₂ = 2 s.

It is required to find the periodic time. Let it is given by T₁. So,

$\dfrac{1}{T}=\dfrac{1}{T_1}-\dfrac{1}{T_2}\\\\\dfrac{1}{T_1}=\dfrac{1}{T}+\dfrac{1}{T_2}\\\\\dfrac{1}{T_1}=\dfrac{1}{18}+\dfrac{1}{2}\\\\T_1=1.8\ s$

So, the periodic time is 1.8 seconds.

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