In a simple pendulum through no friction, mechanical power is conserved. Full mechanical power is a combination of kinetic energy and gravitational potential energy. Together the pendulum swings ago and forth, there is a consistent exchange in between kinetic energy and also gravitational potential energy.

You are watching: The kinetic energy of a pendulum is greatest

Potential Energy

The potential energy of the pendulum have the right to be modeled turn off of the simple equation

PE = mgh

where g is the acceleration as result of gravity and also h is the height. We regularly use this equation to model objects in complimentary fall.

However, the pendulum is constrained by the stick or string and also is no in free fall. Therefore we have to express the height in terms of θ, the angle and L, the size of the pendulum. Thus h = L(1 – COS θ)


When θ = 90° the pendulum is at its highest point. The COS 90° = 0, and also h = L(1-0) = L, and PE = mgL(1 – COS θ) = mgL

When the pendulum is at its shortest point, θ = 0° COS 0° = 1 and h = together (1-1) = 0, and PE = mgL(1 –1) = 0

At every points in-between the potential power can be described using PE = mgL(1 – COS θ)

Kinetic Energy

Ignoring friction and also other non-conservative forces, we discover that in a basic pendulum, mechanical power is conserved. The kinetic power would it is in KE= ½mv2,where m is the fixed of the pendulum, and also v is the rate of the pendulum.

At the highest suggest (Point A) the pendulum is momentarily motionless. Every one of the energy in the pendulum is gravitational potential energy and also there is no kinetic energy. At the lowest allude (Point D) the pendulum has actually its best speed. Every one of the power in the pendulum is kinetic energy and also there is no gravitational potential energy. However, the full energy is continuous as a role of time. You deserve to observe this in the following Physlet on power in a pendulum.

If over there is friction, we have a damped pendulum i beg your pardon exhibits damped harmonic motion. Every one of the mechanical energy eventually i do not care other forms of energy such as warm or sound.

Mass and the Period

Your investigations should have discovered that mass does not impact the duration of a pendulum. One factor to describe this is utilizing conservation of energy.

If we research the equations because that conservation of energy in a pendulum mechanism we discover that mass cancels the end of the equations.

See more: How Many Grape Tomatoes In An Ounce, Grape Tomatoes, 1 Oz

KEi + PEi= KEf+PEf

<½mv2 + mgL(1-COSq) >i = <½mv2 + mgL(1-COSq) >f

There is a direct relationship between the angle θ and the velocity. Because of this, the mass go not affect the behavior of the pendulum and also does not transform the period of the pendulum.