Question

A pendulum can be simply made of a suspended string tied to a weight. If the length of string is measured to be 1 m and the weight is measured to be 0.5 kg, determine its period of oscillation and its frequency of oscillation. Does its period depend on the weight tied to the string?

Answer 1

The time period of the pendulum is 2 sec, and the frequency will be 0.5 and will on depend on weight of the object.

The time period of a basic pendulum is defined as the time it takes to complete one full oscillation and is indicated by the letter "T".

This concept of frequency leads to the simplest frequency formula

Frequency = 1 / T.

T signifies the time it takes to complete one wave cycle in seconds, while f denotes frequency.

The formula for time period of simple pendulum is

Time Period = 2π√(l/g)

As we can see there is no mass term in the formula, Hence we can say that the time period of simple pendulum will not depend on mass or weight of the object tied to the string.

We have given length as 1 m

Time Period = 2π√(1/9.8)

Time Period = 2π×0.319

Time Period = 2 seconds

Time of the Simple Pendulum is 2 seconds.

Frequency = 1 / Time period

Frequency = 1 / 2

Frequency = 0.5 1/second

Frequency of the Simple Pendulum is 0.5

So we can conclude that the Time period of Simple pendulum is 2π√(l/g) and as we can see there is no term of mass, means the simple pendulum will not be depend on mass or weight. The time period came out to be 2 seconds and the frequency came out to be 0.5.

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