Question

The frequency of a second’s pendulum is equal to:
1) 0.5Hz
2) 1Hz
3) 2Hz
4) 0.1Hz

Answer 1

Hint:A pendulum is a device which shows simple harmonic motion and is periodic in nature. It would oscillate from one extreme point to another until it comes to an equilibrium. A second’s pendulum is a pendulum in which the period is exactly two seconds. In one second, it will swing in one direction and in another second it will return.

Complete step by step calculation:
Here, the relation between the frequency and time period is:
$F={\displaystyle \frac{1}{T}}$ ;
Here:

F = Frequency;

T = Time Period;

For negligible mass on a weightless string of Length “L” which is swinging with an infinitesimally small amplitude and without any resistance, the length of the string would be $\left(L={\displaystyle \frac{g}{{\pi }^2}}\right)$ . Here g is the acceleration due to gravity.

Now, we know that the second’s pendulum has a time period of 2 seconds so:

$F={\displaystyle \frac{1}{2}}$;

$\therefore F=0.5Hz$;

Final Answer:Option ”1” is correct. Therefore, the frequency of a second’s pendulum is equal to 0.5 Hz.

Note:The time period is defined as the time required to complete one cycle in an event which is repeating in nature whereas frequency is defined as the number of repeating events per unit of time. For example, if a child’s heart is beating 2 beats per 3 seconds then the frequency would be 0.9 and the time period would be 3 seconds. The time and frequency relation is reciprocal to one another. The seconds pendulum takes 2 seconds, so frequency would be 0.5 seconds.