Assumptions for Simple Pendulum

A simple pendulum is a device that consists of a mass (m) suspended from the end of a flexible, inextensible rod. If the rod’s length (L) and mass are known, then it’s possible to calculate how much energy you need to set in motion – and, just as importantly, how long it will take for this energy to dissipate. 

This article discusses the assumptions used in calculating different types of forces applied to the plane pendulum. This can specify how quickly the system will stop oscillating when released from a certain initial condition, like being placed on a cart at rest.

Plane Pendulum

A plane or rectangular pendulum is one in which the weight of the mass hangs at a right angle to the centerline of the pendulum’s frame. It consists of a support point and mass.

The plane pendulum consists of a string with a weight attached to it. The string is supported by a pivot (or fulcrum) on one end and a fixture (also called an anchor or terminal) on the other end. The pivot point on this simple pendulum is called the “rest” of the pendulum because the object that hangs from it doesn’t move: there is no movement along the length of the string.

It is used for teaching Newton’s Laws; plane pendulums are used to demonstrate that objects maintain their state of motion, and that no acceleration exists without change in momentum (the product of mass and velocity).

Plane of Oscillation of a Plane Pendulum

The plane pendulum swings back and forth in a flat plane that passes through the pivot point. As you may recall from high school physics, the restoring force is the tension on the string .

Newton’s First Law: An object at rest, tends to stay at rest, and objects in motion tend to stay in motion.

Newton’s first law can be demonstrated by using a plane pendulum with an initial velocity. If the plane pendulum is set into motion and released. Without friction, it would stay in motion forever. With gravity not necessarily being the only force involved in the motion of a plane pendulum, it is possible for the plane pendulum to lose some kinetic energy without having any acceleration (a net change m∆v) and, therefore, no change in momentum (m∆v = 0).

Assumptions for Simple Pendulum

• Potential energy = Zero

• The system is frictionless

• The pendulum is in a vertical plane

• Friction is independent of time. This means that the pendulum will always swing back to the equilibrium position, regardless of the time elapsed.

• The string is massless

• The velocity vector is forward

• The mass, in g, is uniform

• The only thing affecting the pendulum is gravity, which has a constant force of 9.8m/s2

Friction Force

Most real plane pendulums are pushed by pushing them instead of using gravity to make them swing.

The vertical part of the string stays frictionless, but the horizontal part does not. When the pendulum is pushed from below, there is a loss of energy in the mass. This loss of energy brings it closer to being at rest. When we push on a plane pendulum, we lose some kinetic energy, but we do not have any net change in momentum because there isn’t any net “push” to overcome.

Forces of Friction or Drag:

The friction force is opposite to the motion. This causes a force to act on the pendulum and slows down its motion. If a forward force is applied to the pendulum by pushing it, there will be a loss of kinetic energy but no net change in momentum. When pushed, it loses some kinetic energy but stays in (or near) its original position and speed.

Gravitational Force

If you have a larger mass and a smaller string, the forces will be greater because of gravity than if you had a smaller mass and a larger string, so this time gravity at the top of the string gets stronger, which causes the pendulum to swing faster. 

The only force acting on the system is gravity. The restoring force is tension on the string and one-half of the mass’s weight. This causes a change in momentum, which causes a change in the direction of motion. 

Gravity on earth is 9.8m/sec2 (in palms)

If you reduce the mass of the pendulum, the force of gravity acting on it will be a little less than normal. This causes a difference in momentum, which causes a change in its direction of motion.

Conclusion

A plane pendulum is an example of a system that does not have constant velocities.

No force can be applied to a plane pendulum to stop it from swinging. If a force is applied to it, the mass of the pendulum will change, and so will its velocity. With some time (we are assuming this is practically instantaneous) and without any other forces involved, the plane pendulum will continue in its original direction of motion with no acceleration or change in momentum at all. This plane pendulum is used to show that inertia works with Newton’s First Law of Inertia.