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Question

How do you double the period of a pendulum?


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Solution

Time period:

  1. Oscillatory motion can be defined as the to or fro motion of an object in a periodic fashion along with an equilibrium position by taking time (T) for one complete oscillation is known as a time period.

The amplitude of oscillatory motion:

  1. The maximum distance traveled from the equilibrium position is known as the amplitude of that oscillatory motion.

Step 1: Given that

The motion of a simple pendulum is a periodic motion in which the bob of a pendulum is oscillating about the mean position within a particular time period.

Time period of a simple pendulum

T=2πLg........1

Here, we can observe that the time period is independent of the mass of the bob of the pendulum, and assuming g constant at a particular position, the only varying quantity is the length of the pendulum.

Let us assume the initial length of the pendulum be(L), so the time period will be(T), now the new length is L'and the time period is 2T, so

2T=2πL'g........(2)

Where, L=the initial length of the pendulum, T=time period, and L'=new length.

Step 2: Further solve the above expression

By dividing the equation 2 by the equation 1 we have,

2TT=2πL'g2πLgL'L=2

Step 3: Calculate the situation when the period of the pendulum is doubled

Squaring both sides we have,

L'L=4L'=4L

Hence, by increasing the length of a simple pendulum by four times the time period will be doubled.


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