Question

What is the period of oscillation of the second pendulum?

Answer 1

Hint The period of oscillation is the time for one oscillation. One oscillation can be termed as the movement of the pendulum back and forth. And the pendulum oscillates with a frequency which depends on the period.

Complete step-by-step answer:
The second pendulum takes one second for one swing and the return takes one second. Therefore the total time taken for the second pendulum is
$1\;{\text{s + }}1\;{\text{s}} = 2\;{\text{s}}$
The frequency of the oscillation is the number of oscillations per second. It can be found by reciprocating the Time period of the oscillation. Thus the frequency of the second pendulum is
$\ f = \dfrac{1}{T} \\\ = \dfrac{1}{{2\;{\text{s}}}} \\\ = 0.5\;{\text{Hz}} \\\ \$
So the second pendulum oscillates with a frequency of $0.5\;{\text{Hz}}$ per second.
Let’s look at how the pendulum works. In a pendulum from a pivot a weight is suspended and it is swinging. When we displace the pendulum from its equilibrium position a restoring force will be created to bring it back to the equilibrium position. The oscillation happens when we release the pendulum. The restoring force and mass of the pendulum will combine and it will cause a back and forth motion. The time taken for a pendulum for one back and forth motion is period of oscillation. The length of the pendulum will affect the period of oscillation. The pendulum oscillating in high frequency will have a low period of time.
Thus the period of oscillation of the second pendulum is $2\;{\text{s}}$.

Note As the name indicates the second pendulum is called because its period of oscillation is two seconds. Thus one second for one swing and return takes only one second. That’s why they are called the second pendulum.