Physical Pendulum

A pendulum is a weight, like a ball or the bob of a clock’s long pendulum, suspended from a fixed point by an elastic cord. The swinging motion of the pendulum can be used to tell time, measure angles, and as proof/disproof for perpetual motion.

After a time, this angular momentum rotates the pendulum back to its original position.

This blog post will explain physical pendulums, friction, the physics of the physical pendulums, and the formula for calculating the time period of a pendulum. Hopefully, this provides some insight into understanding physics within everyday life.

Physical Pendulum

The physical pendulum is a weight that is attached to a string. The string is not very elastic and can be almost inelastic, like a piece of thread.

The mass must have a certain amount of angular momentum about the pivot point for the pendulum to swing back and forth. This requires that the mass be travelling at either its maximum or zero speed at some point in its motion. The maximum speed that a pendulum achieves occurs when it swings from directly overhead (the highest point).

Features of a Physical Pendulum:

The physical pendulum has kinetic energy. On the left-hand side, some of the kinetic energy converts into potential energy (the gravitational potential energy due to the mass of the weight). 

• The physical pendulum has potential energy at equilibrium. For example, if we held a weight straight down, it would have zero potential energy and would be at rest. The equilibrium of a pendulum occurs when the weight is at its lowest point, about to swing back up. At equilibrium, the weight’s potential energy is equal to the gravitational potential energy of all other masses on the Earth’s surface.

• The physical pendulum has conservative energy. The work done by an external conservative force on a system increases the internal energy of that system (the kinetic and potential energies). Work done is equal to the change in kinetic energy and potential energy.

• The physical pendulum has reversible work done upon the system. Work done by a conservative force at the end of a pendulum’s swing equals the energy transferred to or from the system during that period.

• The physical pendulum has kinetic energy. Some of the kinetic energy converts into potential energy (the gravitational potential energy due to the mass of the weight).

The Formula of Time Period of Pendulum

The amount of time it takes a physical pendulum to swing back and forth is called period.

The formula of time period of the pendulum can be written as follows:

T= 2π√l/g

Where: T = time period of a pendulum, in seconds. 

l = length of the pendulum, in meters. 

g = acceleration due to gravity, about 9.8 m/s2. 

Friction:

For a pendulum to swing, it needs to overcome friction. There are two types of friction that affect the pendulum: static friction and kinetic friction.

• The coefficient of static friction is the force required for an object to move when it is at rest on a surface perpendicular to the direction of motion (like the string).

• The coefficient of kinetic friction is the force required for an object moving on a surface to keep it from sliding concerning the surface.

The coefficient of static friction depends on the type of surface and is difficult to determine for any individual apparatus.

Force

In a pendulum, the force acting on it at equilibrium is called the tension force T, which has a magnitude dependent on how high the weight is when at rest and how quickly it is swinging. A falling pendulum has no kinetic energy, so its potential energy (the work done by gravity) is zero at equilibrium.

The downward force T is the sum of several forces.

The gravitational force Fg (the weight is at rest, and the string is perpendicular to the direction of motion), which acts downwards, has a magnitude equal to the weight W acting vertically down upon the object.

In order for a pendulum to maintain oscillation, the forces acting on it must be in equilibrium. If the forces acting upon any oscillating system are not in equilibrium, then energy is lost through damping.

At equilibrium,

F = -mgsinθ

Conclusion

A pendulum is one of the easiest oscillators to analyse since it is so simple yet still oscillates perfectly. A lot of the effort you put into studying a pendulum will be very useful later on in your studies.

Studies have shown that a mechanical pendulum is an excellent way to measure the time it takes for an oscillating system to return to its equilibrium position.

The rate at which a pendulum swings back and forth without gravity can be measured in many ways. It is, however, difficult to determine for any individual apparatus.