Pendulum

There are many types of pendulums. The most simple one is a metal ball also called a bob suspended from rigid support by a long thread so that the bob may swing freely from side to side.

If a pendulum’s length is kept constant, each swing (or oscillation) will take precisely the same time. A pendulum’s oscillation period is always the same. A simple pendulum may be made by attaching a one-meter long thread to a bit of metal ball known as the bob and allowing it to swing freely from a stable stand. The bob is at the mean position when the pendulum is at rest. If the bob of this pendulum is pulled to one side and then released, it will continue to oscillate back and forth like a swing.

The bob begins at position X, which is the average position. Consider pushing the bob to the right to position Y and then releasing it. Returning to position Z, on the other side of the mean position X, and continuing this back and forth motion between the two extreme locations Y and Z will be detected. The basic pendulum is also known as an oscillating pendulum (or vibrating). The to-and-fro motion of a simple pendulum exemplifies periodic motion, also known as oscillatory motion.

Theory of the Simple Pendulum

A simple pendulum is a point mass suspended from a point by a massless thread and allowed to swing back and forth in space. Considering that a pendulum is suspended from a string with a long length and a mass that is comparable to the diameter and mass of a tiny metal sphere, it can be appropriate to imagine a tiny metal sphere with a large diameter and a large mass. Pendulums swing back and forth regularly when they are set in motion. The time it takes to complete one full oscillation is the period T. Another useful measure for defining periodic motion is the oscillation frequency. The frequency f of an oscillation is the reciprocal of its period, f = 1/T, T = l/f. The number of oscillations occur per unit time should be equal to the frequency f.

In the same way, frequency is inversely proportional to time. A mass oscillates at a maximum amplitude if it gets shifted out of equilibrium from its equilibrium position. A restoring force returns a pendulum to its equilibrium position after it has been moved from its equilibrium point. When the pendulum goes beyond the equilibrium point, the restoring force reverses direction, guaranteeing it returns to the equilibrium position. The relationship is met if the restoring force F is equal to and opposing the displacement x from the equilibrium position.

F = -k * x  ————————————–(1)

As a result, the pendulum’s motion will be simple harmonic motion, and its time period formula may be calculated using the simple harmonic motion period equation.

T = 2π √(m/k) ————————————–(2)

If the motion’s amplitude is maintained small, Equation (2) will be satisfied, and the motion of a simple pendulum will be simple harmonic motion, allowing Equation (2) to be used.

Length of the Pendulum

The thread length from the point of suspension to the center of the bob determines the pendulum’s length. The period of a pendulum is determined by its length. A pendulum’s period increases as its length increases. A fixed-length pendulum has a steady period.

Oscillations

The complete back-and-forth movement of the pendulum bob is referred to as an oscillation. One oscillation may be counted starting with one of the bob’s extreme positions or the mean position. The movement of a simple pendulum bob from its extreme point Y to Z and back to Y is an example of oscillation. The bob’s move from its mean position of X to Y, then from Y to Z, then back to X is likewise an oscillation.

Time-Period

The period of a pendulum bob is the amount of time it takes to complete one entire oscillation. The time it takes bob to move from position B to C and return to B is the period of a pendulum. Bob spent the same amount of time traveling from point A to point B, then from B to C, and finally back to point A. To find the time taken by a single oscillation, we measure the time taken by numerous oscillations (or time). By dividing the total time by the number of oscillations, we may get the pendulum’s time for one oscillation (or time-period).

Amplitude

The pendulum’s amplitude is the maximum deviation of the bob from its mean position on either side when it oscillates (or swings) back and forth. The distance XY measures the amplitude of the pendulum. The pendulum’s amplitude is also equal to the distance XZ. The time it takes for one full oscillation (or time-period) is the same regardless of the magnitude of a pendulum’s oscillations. A pendulum of a certain length completes one oscillation simultaneously every time. A fixed-length pendulum has a constant period. Consequently, periodic oscillation has been used to create pendulum clocks for time measurement.

Conclusion

A simple pendulum may be made by attaching a one-meter long thread to a bit of metal ball known as the bob and allowing it to swing freely from a stable stand. The most simple one is a metal ball also called a bob suspended from rigid support by a long thread so that the bob may swing freely from side to side. The to-and-fro motion of a simple pendulum exemplifies periodic motion, also known as oscillatory motion. If the bob of this pendulum is pulled to one side and then released, it will continue to oscillate back and forth like a swing. The bob is at the mean position when the pendulum is at rest. Returning to position Z, on the other side of the mean position X, and continuing this back and forth motion between the two extreme locations Y and Z will be detected.