Forced Oscillations and Resonance

The forced periodic oscillation is that the system does not oscillate at its natural frequency ω, but at the frequency ωd of the external mechanism; free oscillations disappear due to damping. The most common example of forced swing is when a child periodically presses his foot on the ground on a garden swing (or someone else periodically pushes the child) to keep the swing. 

Resonance phenomena happen with a wide range of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, atomic resonance(NMR), electron turn resonance(ESR), and resonance of quantum wave capacities. Complete frameworks can be utilized to produce vibrations of a particular recurrence (e.g., instruments) or choose explicit frequencies from a perplexing vibration containing numerous frequencies. Now, let’s understand it in more detail.

Free Oscillation:

The free oscillation has a constant amplitude and period, and no external force is required to set the oscillation. Ideally, free oscillations will not be damped. But in an all-natural system, damping will be observed unless and until any constant external force is provided to overcome the damping. The amplitude, frequency, and energy are constant in such a system.  

Free oscillation is an ideal condition for the movement of particles not to be affected by any external resistance. It is a movement with a particle’s natural frequency and constant amplitude, energy and period. It is ideal because every oscillating object will interact with external conditions in some form, resulting in energy loss. An example of free oscillation is the movement of a simple pendulum in a vacuum.

Forced Oscillation:

When an object vibrates under the influence of external periodic forces, it is called forced vibration. Here, the oscillation amplitude undergoes damping but remains constant due to the external energy provided to the system. For example, when you push someone on a swing, you must constantly push them so that the swing does not decrease.

Forced oscillations in particles result from continuous application of external force to help them maintain a constant amplitude, time, and frequency of motion. In these cases, the damping force is offset with the help of artificial external conditions, thereby maintaining periodic motion. The motion that embodies the definition of forced oscillation is the vibration in the speaker caused by the current.

Forced oscillations happen while a swaying framework is driven by an occasional power outside the wavering framework. In such a case, the oscillator is forced to move at the frequency νD = ωD/2π of the driving force. The fascinating part of a forced oscillator is its reaction, the amount it moves to the forced main thrust.

Calculation of Oscillation

A few estimations characterize oscillation. Here, we have clarified every boundary with their unit of measure and the formulae to ascertain their esteem and see how to characterize oscillation motion.

• Period of Oscillation 

The time taken by an oscillating body to finish one pattern of movement is called its oscillation period. It is by and largely estimated in seconds and is signified by T.

Here are how to ascertain the time of oscillation 

T = 2π √(L/g)

Where L represents the length of a pendulum and g is the acceleration due gravity.

• Frequency of Oscillation 

The number of motions a body can finish in one second is known as its frequency of oscillation. The SI unit of frequency is Hertz and is represented by f.

You can work out the value of f with its connection to period T of oscillation as follows:

f = 1/T

• Amplitude of Oscillation 

Amplitude is the greatest measure of displacement of an oscillating body from its mean position. Its value is measured in meters, and it is denoted by A.

With a known worth of A, the displacement x is given as,

                             x = A cos 2πft

Where,

             ‘t’ is the time of the oscillation.

f is the frequency of the oscillation.

Resonance:

The phenomenon of resonance is both recognisable and marvelously significant. It is natural in circumstances as straightforward as developing a large amplitude in a child’s swing by providing a little power simultaneously in each cycle. However, simple for all intents and purposes, it is critical in numerous gadgets and many sensitive physics tests. This phenomenon is utilized universally to develop a vast, measurable reaction to a minimal disturbance.

Due to this large-amplitude oscillation, the above first example may fail. When tuning one system with another system, you can see that at the resonance frequency, the vibration amplitude of the strings is the largest. These oscillations of large amplitude at the resonance frequency are due to the vibration energy.

Conclusion:

In forced vibration, the energy drawn from the source can increase the potential or kinetic energy of the system. When the frequency of the external periodic force is adjusted so that the amplitude in the system rises to the maximum value, we call this resonance “amplitude resonance”. In this case, the system’s potential energy is at its maximum. When the frequency of the external periodic force is adjusted to increase the speed to the maximum value, this phenomenon is called “velocity resonance”.