Question

What is the second pendulum?

Answer 1

Hint: A second’s pendulum is the pendulum having time period two seconds and length equal to one meter. By substituting all the values in the formula for the time period we can find out the value of the length of the second's pendulum.
Formula: \[T=2\pi \dfrac{\sqrt{l}}{\sqrt{g}}\]

Complete answer:
We can describe a pendulum as a weight suspended from a pivot which can swing freely. When a pendulum is displaced from equilibrium position, it is subject to a restoring force due to gravity which accelerates it back toward the equilibrium position. When the pendulum mass is released, the restoring force acts on the pendulum's it and causes it to oscillate about the equilibrium position, back and forth. The time taken by the pendulum for one complete cycle, a left swing and a right swing, is called the period.
As we know that the second's pendulum has a time period of 2 seconds and it performs oscillatory motion. Second’s pendulum takes exactly one second for each swing in either direction and two seconds for complete vibration therefore it is known as second’s pendulum .The length of the seconds pendulum is one meter,\[l=1m\].We can find its length by the formula of Time period of a pendulum given by:
\[T=2\pi \dfrac{\sqrt{l}}{\sqrt{g}}\] ………(1)
 where the \[l\] is the length of the pendulum, \[g=9.8m{{s}^{-2}}\]and the time period \[T=2\sec \]. By putting these values in equation (1) we will get
 \[T=2\pi \dfrac{\sqrt{l}}{\sqrt{g}}\]
 \[\begin{align}
  & \Rightarrow 2=2\pi \dfrac{\sqrt{l}}{\sqrt{9.8}} \\
 & \Rightarrow l=\dfrac{4\times 9.8}{4{{\pi }^{2}}} \\
 & \therefore l=1m \\
\end{align}\]
The length of the pendulum string depends upon the acceleration due to gravity on the surface of that place. For example, the length of second’s pendulum on the surface of the moon is $\dfrac{1}{6}m$We can calculate this by substituting ${{g}_{m}}=\dfrac{1}{6}{{g}_{e}}$.Thus, we can say that length of second’s pendulum varies from place to place.

Additional information:
Generally, there are four types of pendulum:
Compound Pendulum: It is a rigid body suspended from a fixed horizontal axis which can oscillate in a vertical plane. It is also known as physical pendulum.
Simple Pendulum: It is similar to the compound pendulum but the mass is concentrated in a single point and oscillates back and forth in the vertical plane. The mass point is connected to a horizontal axis with a weightless chord. It is also known as mathematical pendulum.
Conical Pendulum: It is similar to a simple pendulum but the weight suspended by the chord moves in uniform speed around the circumference of a circle in the horizontal plane.
Torsional Pendulum: It is a disk fixed to a slender rod. The rod is fastened to a fixed frame. The disk oscillates back and forth when it is twisted.

Note:
One must remember that the above given formula is for Compound Pendulum, Simple Pendulum and Conical Pendulum. For torsional pendulum, the time period formula is different.