When we pull the pendulum back by an angle (amplitude) of Ɵ, we can then represent these forces as a right triangle:
We can see that,
since by Newton’s second law, the force of gravity is equal to mass (m) multiplied by acceleration due to gravity (g).
What factors influence the period of a pendulum?
When a pendulum is hanging straight down and is not moving at all, it is said to be in equilibrium. At this point, all the forces acting on it are balanced. But, if you were to pull the pendulum away from the equilibrium and let go, it would swing back and forth towards the equilibrium position as the forces are no longer in balance.
In reality, factors such as friction at the pivot point and air resistance cause the pendulum to slow down until it eventually stops.
So as to avoid getting into some very complicated calculus, let us consider a more perfect scenario where the elements of friction and air resistance are negligible. In this scenario, a given pendulum’s period would always be the same because it would never slow down.
So what factors influence the period of a pendulum? Intuitively, you would think maybe,
●the mass of the bob (m)
●the length of the wire (l)
●the amplitude of angular displacement (Ɵ): the angle between the wire and the equilibrium point
Would you be surprised to learn that the period of a pendulum depends on nothing other than the length of the pendulum’s wire?
We can derive this conclusion using waves.
For small angular displacements, a pendulum demonstrates what is called simple harmonic motion.