Question

The time period of a second’s pendulum:
A.) 1 second
B.) 2 seconds
C.) 3 seconds
D.) 4 seconds

Answer 1

Hint: Second’s pendulum is a simple pendulum and it takes one second for a swing in one direction.

Complete step by step answer:
We can see second’s pendulum in vintage clocks. In these clocks, one second will take for a swing in one direction and one second for the next swing. So, it reaches extreme position twice in one oscillation. Hence the time period of second’s pendulum is 2 seconds. So, the correct answer is option (B). The frequency of a second’s pendulum is 0.5 Hz.

Additional information:

If we are considering the time period of second’s pendulum as 2 seconds, we can simply calculate the length of the pendulum.
As we know, we can use the time period equation of a simple pendulum for the calculation of length.
Time period, \[T=2\pi \sqrt{\dfrac{l}{g}}\], where l is the length and g is the acceleration due to gravity.
We can assign T as 2 seconds and acceleration due to gravity as 9.8 m/s²
\[2=2\pi \sqrt{\dfrac{l}{9.8}}\]
So the length of the second’s pendulum, \[l={{\left( \dfrac{2}{2\pi } \right)}^{2}}\times 9.8\]
\[l={{\left( \dfrac{1}{\pi } \right)}^{2}}\times 9.8\]
\[l=0.9929\]
So that, \[l\approx 1m\]

The second’s pendulum has a constant length, around 1 meter in everywhere on the earth.
The diagram shows the motion of second’s pendulum.

The second’s pendulum is a type of simple pendulum. A pendulum is a freely swinging weight suspended from a pivot. A slight displacement in the sideways will bring acceleration towards the equilibrium position. When the weight is released, the restoring force and mass of the pendulum makes oscillations about the equilibrium position. It will cause swinging of the pendulum.

Note: Do not make any inferences from the name of second’s pendulum. For a swing in a particular direction, the second's pendulum takes one second. So, the time period for a complete cycle is two seconds.