Simple pendulum is a device who can execute simple harmonic
motion. It consists of a metal bob of heavy in mass but point in size.
Obviously it shall have a higher density. We can define simple pendulum as a
heavy and point sized mass suspended
from a rigid support with the help of a in extensible string.

We can show that simple pendulum is in simple harmonic motion and we can also derive a equation for the time period of it as shown below. Consider that we have applied a small force therefore the bob is displaced by a small angle with the vertical. At that given instant, in the string of length

We can show that simple pendulum is in simple harmonic motion and we can also derive a equation for the time period of it as shown below. Consider that we have applied a small force therefore the bob is displaced by a small angle with the vertical. At that given instant, in the string of length

**l,**there is a**force acting towards the point of suspension and that is called as tension. Being the mass is having a gravitational influence on it its weight is always acting in the downward direction. We can resolve the weight into components as shown just because it is a vector .**
It can be notice that this is
small vibratory motion is a part of bigger rotatory motion and hence there must
be some torque acting on it. We can calculate this turning effect of force using
by both the components as shown.

Here we are getting a term called
moment of inertia which is similar to the mass of a body who is in translatory motion. As mass is the deciding factor to identify that how difficult
it is to put a body translatory motion, in rotatory motion we are having a
similar physical quantity called a moment of inertia.

If moment of inertia is more it will be difficult to put the body in rotatory motion and vice versa.

If moment of inertia is more it will be difficult to put the body in rotatory motion and vice versa.

The further simplification of the equation is as shown below.

We can identify that the time
period of a simple pendulum is independent of the mass of the bob. The length
of the pendulum is the distance between the point of suspension and the centre of mass of the bob.

Therefore though the time period
is independent of the mass it depends on the length of the pendulum.

**Problem and solution**

If the length of a simple
pendulum is increased by 69% of its time period is affected?

While solving this problem we can assume that the experiment is done at the same place and hence acceleration due
to gravity is constant. Therefore the length of the pendulum under the Squire
route is directly proportional to the time period. The problem can be solved as
shown below.

**Problem and solution**

If the length of the pendulum is
changed by 5% calculate how it’s time period is affected?

Solving of this problem shall be
done differently from the previous
problem. It is simply because he is a variation in the length is a small
percentage and hence we can apply approximations concept rather than
calculating in lengthy way of a previous
problem.

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