Question

The frequency of a second's pendulum is
A) 0.5 Hz
B) 1.0 Hz
C) 1.5 Hz
D) none of these

Answer 1

Hint:A second’s pendulum is a special type of pendulum which takes exactly one second to complete its swing in one direction. Hence, for finishing one complete oscillation it will take 2 seconds.

Formula used:
Time period of any pendulum is the total time required by the pendulum to finish its one complete cycle. And frequency is the number of times a pendulum oscillates within 1 second. So the relationship between time period and frequency is given as:
$f = \dfrac{1}{T}$.............................(1)
Where,
f is the frequency of oscillation,
T is the time period of the oscillation.

Complete step by step answer:
Given: Second’s pendulum takes one second to complete its single swing in one direction, so its time period is $T = 2 \times 1s = 2s$.

To find: The frequency of the pendulum.

Step 1
Substitute the given value of T in eq.(1) to get the value of f as:
$
  f = \dfrac{1}{{2s}} \\
  \therefore f = 0.5Hz \\
 $

Correct answer:
The frequency of the second's pendulum is (a) 0.5 Hz.

Additional information:
Since, half oscillation of a second’s pendulum takes exactly one second so the second's pendulum was widely used in quality clocks. Second’s pendulum is precisely 0.994 m long. Around 1680 long narrow clocks were built around these pendulums and they were known as ‘grandfather’s clock’.

Note: There is an important point where a student can make mistakes while calculating the time period of second’s pendulum. You must remember that the time period of a second's pendulum is not one second. It’s actually the time swing in one side, i.e. half period. Hence, the total time period is 2 seconds not 1 second.