Simple pendulum and Second’s Pendulum

A pendulum is stated as a device in which the weight (bob) is suspended along with a centre point with the help of a string or any inelastic strand so that it can oscillate freely. When a pendulum is oscillating from its mean position, it is subjected to the restoring force, equal to the magnitude of displacement and opposite to the direction of displacement. The time taken for one complete swing for the left and right is called a period. The period depends on the length of a pendulum, the amplitude of its swing, and slightly on the weight distribution. Let’s look at a simple pendulum before going into the second pendulum.

Definition of a simple pendulum

A simple pendulum is a device in which a light inelastic string suspends the point mass at a fixed point. The simple pendulum motion is assumed to be a simple harmonic motion when the phase angle is small and the pendulum is not performing the circular motion.

The formula for some time of Simple Pendulum

Consider a bob of mass ‘m’, which is attached by an inelastic string of length ‘L’ when the ø bob moves from its mean position, and three forces are acting on it,

Let Time period T= time required to complete one oscillation.

At the mean position, the time period will be T0​=mg.

For SHM, the displacement ‘x’ will be small, for which the angle form between fixed and extreme positions will also be small.

The restoring force of the bob will be, 

Restoring force= -ma

Therefore,

Restoring force =−mgsinθ    ……..(mgsinθ is the acts opposite to the restoring force)

Definition of Second Pendulum

The simple pendulum, which takes two seconds for completing the front and back motion in a straight line, is called the second’s pendulum. We can say it takes one second to move from its mean position to the right extreme and another one second to move from its mean position to the left extreme. Thus, in total, it takes two seconds to complete the whole oscillation.

Length of a second’s pendulum.

Time period (T) for the simple pendulum,

Thus, the length of the second’s pendulum must be 1 metre as per the above derivation. 

The pendulum’s length is defined as the distance of the centre of gravity of the bob to the rigid support.

Use of the pendulum

The second pendulum is also named the Royal Pendulum. It is widely used in quality clocks since it greatly increases the clock’s accuracy to a great extent. William Clement was the first to make the long narrow clocks around these pendulums. These clocks made around the pendulum popularly became known as grandfather clocks at that time. 

A simple pendulum is the seismograph, metronomes, and amusement park rides.

Solved examples

Conclusion

Thus, it can be concluded that:

1. The second’s pendulum is the pendulum compulsory having the length of 1 metre.
2. A second’s pendulum is used in the quality watches to get the accurate time.
3. For the second’s pendulum to be in SHM, the displacement of the bob from the main position should be small.
4. Since the second’s pendulum is accurate and easy to use, it is used in science laboratories; the second’s pendulum is used to carry out the experiment related to SHM.
5. The second’s pendulum is the simple pendulum requiring two seconds to complete oscillation from its mean position.