An ideal pendulum system always contains a stable amount of mechanical energy, that is, the total of kinetic plus potential energy. As the pendulum swings back and forth, the balance between the two types of energy changes constantly. At some points in its swing, the pendulum has more kinetic energy.

A pendulum at rest is in a position of stable equilibrium. But a swinging pendulum is not in equilibrium at all. The force on it varies periodically, becoming zero when it passes through the equilibrium point.

For a swinging pendulum there is a net force and hence the pendulum bob accelerates. Thus at the bottom of the swing, the net force (Tension – Weight) is responsible for the centripetal acceleration. Tension – Weight = m acentripetal. A swinging pendulum is never in equilibrium (i.e. there is always a net force).

When a swinging pendulum passes through its equilibrium position its force diagram is momentarily balanced. 2. The speed of a wave depends on the properties of the medium it is traveling through, and on the amplitude of the wave.

For the motion of a child on a swing, the bottom of the arc (when the swing hangs straight down) is the point of stable equilibrium. The point of stable equilibrium for a weight on the rubber band is the location at which the weight would hang if it was very slowly lowered.

Finally, the angle that the pendulum swings through (a big swing or a small swing) does not affect the period of the pendulum because pendulums swinging through a larger angle accelerate more than pendulums swinging through a small angle.

Period Of Oscillation The time taken for one complete oscillation is called Period. Second.

When we displace a pendulum from its equilibrium position, it oscillates to and fro about its mean position. Eventually, its motion dies out due to the opposing forces in the medium. This type of motion is known as forced simple harmonic motion. …

Forced vibrations occur if a system is continuously driven by an external agency. A simple example is a child’s swing that is pushed on each downswing. Of special interest are systems undergoing SHM and driven by sinusoidal forcing.

The damping ratio is a measure describing how rapidly the oscillations decay from one bounce to the next. The damping ratio is a system parameter, denoted by ζ (zeta), that can vary from undamped (ζ = 0), underdamped (ζ < 1) through critically damped (ζ = 1) to overdamped (ζ > 1).

Nature of free vibrations – result Amplitude and frequency of a freely vibrating body remains constant. They do not lose or gain any energy in the process. Free vibrations for sound can occur only in vacuum. It is not possible to practically realize free vibrations.

From the dawn of life on Earth, the planet has had what’s known as “natural frequency.” The Earth’s natural frequency is called the Schumann Resonance, which pulsates at a rate of 7.83 hertz. It surrounds and protects all living things on the planet.

The frequency of damped vibrations remains same but the amplitude decreases gradually.