Simple Pendulum
We almost have certainly seen pendulum clocks in movies, museums or even at someone’s house.
As the name suggests, a Pendulum clock has a pendulum oscillating in it.
The electronic clocks that are used often, run on the battery or electrical supply.
But the pendulum clock runs on the oscillation of the pendulum which is a closed approximation of the simple pendulum.
Let’s discuss the simple pendulum.
Consider a rubber ball is held at a certain height above the ground.
It has a certain amount of potential energy, which rapidly converts to kinetic energy after it is dropped.
Similarly in the pendulum clock, a weight attached to a string falls down steadily.
When the bob is at highest, it has maximum potential energy.
As it accelerates down towards its lowest point, this potential energy is converted into kinetic energy.
And then as the bob climbs up again back to the potential energy.
Therefore the bob swings back and forth, it repeatedly switches its energy back and forth between potential and kinetic.
Sometimes that works this way is called a harmonic oscillator and its movement is an example of simple harmonic motion.
If there is no friction or drag, a pendulum would keep on moving forever.
In reality, each swing sees friction and drag steal a bit more energy from the pendulum and it gradually comes to halt.
Hence, a pendulum is a rod hanging vertically from its top (bob) that swings from side to side due to the force of gravity
$Mg$
.
This pendulum of length
$L$
executes to and fro motion at angle
$θ$
so it has two positions and one mean position with respect to point
$S$
.
Suppose at position 1 with angle
$θ$
, we have two forces, one is tension in string
$F$
and another is a force of gravity
$mg$
.
Now the force of gravity has two components of forces acting on the bob.
These components are called the radial and tangential forces.
The force
$F$
balances the one component of force so along the string, there is no motion.
Therefore the motion is due to another component of the force.
Due to the circular motion, the torque is generated.
So the torque is the twisting force that tends to cause rotation. It is represented by
$τ$
.
Now the torque for the radial component is zero because the
$θ$
is zero here.
And the torque for the tangential component is.
The net torque is the addition of the radial torque and tangential torque.
The moment of inertia
$I_{s}$
of a point mass about the pivot
$S$
is.
The time period
$T$
of the pendulum is.
Put the value
$I$
. Then, we get the time period,
$T$
.
Revision
A pendulum is a rod hanging vertically from its top(bob) that swings from side to side due to a force of gravity.
It has a certain amount of potential energy, which rapidly converts to kinetic energy after it is dropped.
This is the free body diagram of a simple pendulum.
The torque and time period of the pendulum is.
The End