In classical mechanics, pendulums are one of the interesting concepts to study the motion of the object.
When a body is supposed to suspend from a fixed point that is free to move back and forth is called a pendulum. Simple and physical pendulums are pretty similar, but some properties may differ. Let us study the difference between simple and physical pendulum in this post.
You may have seen the simple pendulum in the laboratory.
A bob of certain mass ‘m’ is suspended from a fixed point with the help of an inextensible cable that is supposed to swing back and forth is said to be a simple pendulum.
Have you ever seen any object hanging at a fixed point of suspension around you? If yes, then these are nothing but the physical pendulum.
Any object hanging freely and making back and forth motion is the same as the simple pendulum, but they are not supposed to hang with the help of string or cable are called the physical pendulum.
Difference Between Simple And Physical Pendulum.
Even though simple pendulum and physical pendulum sound similar, there are some differences between them, that are listed in the below table.
|Simple pendulum||Physical pendulum|
A simple pendulum is considered as an ideal model because some times it is difficult to achieve in reality.
|A physical pendulum is a realistic model of the pendulum; it has finite body and shape.|
|Suspension||A simple pendulum needs a tread or a string to suspend from a rigid support.||A physical pendulum does not need any string for the suspension.|
|Tension||There is a tension force acting on the string, which helps the object to suspend.||As a physical pendulum does not need any string for the suspension, there will be no tension.|
|Time period||The time period is depends on the square root of the ratio of length of the pendulum and the acceleration due to gravity.||The time depends on the square root of 2/3 ratio of of length and the acceleration due to gravity. |
|Mechanical energy||Mechanical energy is conserved at every oscillation.||Here also mechanical energy is conserved at every oscillation.|
|Oscillation||A simple pendulum oscillates with a large angle in short interval of time.||The angle of oscillation of physical pendulum is small.|
|Gravity||Gravity acts at the center of the bob of the pendulum.||Gravity acts towards the center of mass of the physical pendulum.|
|TorqueWhen a simple pendulum is free to rotate, the torque is due to gravity or angular acceleration.||The physical pendulum rotates freely due to the torque applied to the center of mass.|
Some facts related to the simple and the physical pendulum.
- The gravitational force acts as a restoring force for both simple and the physical pendulum.
- The string used in the case of a simple pendulum should be unstretchable and mass-less.
- In a physical pendulum, the moment of inertia is not equal to the product of mass and the square of the object’s length, as in the case of a simple pendulum. The center of mass is at the half the length, so that the moment of inertia at the center is
The moment of inertia at the point of suspension is
The total moment of inertia is given by I = Ic+I0
- The point of oscillation can be changed if the point of suspension changes.
- The most effective way to calculate the acceleration due to gravity is “physical pendulum”. It is given as;
- In a simple pendulum, the rise in the temperature may cause a change in the length. The change in length given by
L’ = L (1+α∆θ)
where; α and θ are the temperature coefficients.
- If we treat the physical pendulum as a simple pendulum, then we can consider the mass is concentrated only at a single point so that the time period of both the pendulum will be the same.
Important terms to remember
The mean position of a pendulum is the position where the pendulum is suspended vertically, and the bob is at rest so that it can be chosen as a reference point for the calculation is called the means position.
The amplitude of the pendulum is the distance traveled by a pendulum from its mean position to one extreme position.
The Center of mass of a pendulum is a point on the body where the entire mass of the system is concentrated.
Frequently Asked Questions
What are the factors that influences the pendulum to increase its time period?
To increase the time period of the pendulum the following factor influences.
- The length of the suspension string
The to and fro motion increases as the length of the string increased, this helps to increase the time period.
- The angle
When the pendulum makes a greater angle, the amplitude increases, the falling time of the pendulum becomes less, and the time period increases.
Does the oscillation of the pendulum depend on the mass?
Oscillation of the pendulum is completely independent of the mass.
Although mass has an effect on inertia, it does not make any change in the force that acts through the pendulum. So that oscillation remains the same even if mass is bigger or smaller.
Is there any effect on the pendulum due to air resistance?
In the absence of air resistance, the pendulum oscillates continuously with constant amplitude.
When a pendulum is oscillating with a certain time period, the air resistance resists the bob to accelerate and hence gradually decreases the time period. The decrease in the time period makes the pendulum come back to its original rest position.
Explain the action of mechanical energy of the pendulum.
In simple frictionless pendulum, the mechanical energy is always conserved, and it is the sum of kinetic and the gravitational potential energy acting on the pendulum.
As the pendulum swings, there will be constant energy exchange takes place. The exchange of kinetic energy and the gravitational potential energy takes place at each and every oscillation. This mechanical energy involved in the action helps to maintain the constant period of the pendulum.