We see several instances of vibrating or oscillating objects in our lives. For example, a guitar string, a swing, or even a car passing over a rough patch of road. All of these oscillations fall within this category.
Forced Oscillations and Resonance
A system is said to be executing free oscillations if it vibrates with its own natural frequency without any help of external periodic force.
What are Forced Oscillations?
When an external periodic force causes an object to oscillate, this is known as forced oscillation. This indicates that something is constantly pushing it to move back and forth slightly than causing it to vibrate on its own.
Think about it as pushing a swing. Free oscillation occurs when we push it once and then release it, causing the swing to progressively slow down and stop due to friction and air resistance. However, if we continue to push the swing at regular intervals, it will continue to move. Because our hands are continuously applying a periodic force, this oscillation is forced.
Key Features of Forced Oscillations:
1.External Periodic Force: A force supplied to the system that recurs after a predetermined amount of time.
2. No Natural Frequency Motion: The system does not oscillate at its own natural frequency, but at the frequency of the external force.
3. Steady-State and Transient: The item will behave in a variety of ways at first, but it will eventually settle into a steady pattern that corresponds to the external force’s frequency.
Damping in Forced Oscillations
Resistance of some form, such as air resistance or friction, is a constant in systems. As a result, the oscillations’ amplitude or size gradually decreases. We called as this phenomena as dampening.
When it comes to forced oscillations, damping is vital. Even if the external force is quite regular, the system cannot build up a significant amplitude if the damping is too high.
Resonance: The Magic of Matching Frequencies
Resonance is among the most interesting results in forced oscillations. This occurs when the external force’s frequency and the system’s inherent frequency coincide.
Resume our swing. There is an inherent rhythm to each swing. Resonance is achieved when we push the swing in time with that rhythm; the swing gets higher and higher.
Definition of Resonance:
Resonance is the phenomenon wherein an oscillating system’s amplitude reaches its maximum when the external force’s frequency coincides with the system’s inherent frequency.
Resonance: The phenomenon of increase in frequency of amplitude when driving frequency is close to natural frequency is called resonance.
Resonance causes disaster during earthquake. When the natural frequency of the building becomes equal to the frequency of the periodic vibrations present in the earth during earthquake, then the building starts vibrating with large amplitude and hence gets damaged.
Examples of Resonance:
Musical Instruments: A guitar string vibrates strongly when it resonates with the body of the guitar, amplifying the sound.
Radio Tuning: Radios operate by adjusting to a station’s resonant frequency.
Glass Breaking by Voice: If a singer’s voice resonates with the glass’s inherent frequency, they can break a glass.
Bridges and Buildings: To keep structures from collapsing in the case of an earthquake or severe wind, engineers must maneuver clear of resonance.
Amplitude vs Frequency
The curve appears as a strong peak at the resonant frequency when the amplitude (the size of the oscillation) is plotted against the external force’s frequency. The damping decreases with increasing peak height and sharpness.
Summary
Forced oscillations and resonance are important concepts in engineering, music, and even nature. Knowing them enables us to create better structures, machinery, and even musical instruments. Resonance can be helpful, but if left unchecked, it can also be harmful.
When a system is disturbed and then vibrates on its own without any outside force, this is known as a free oscillation (like a pendulum left swinging). When a constant external periodic force is given to the system, such as when someone pushes a swing on a regular basis, forced oscillations occur.
A force that repeats its pattern at regular intervals is known as a periodic external force. This type of force continuously pushes or pulls the system to keep it moving during forced oscillations.
When the external force’s frequency coincides with the system’s inherent frequency, a state known as resonance occurs, which results in an extremely large oscillation amplitude.
Yes, there are circumstances in which resonance can be dangerous. If the vibrations from wind or earthquakes coincide with their natural frequency, for example, it may cause bridges or structures to tremble strongly. Engineers put a lot of effort into preventing such circumstances.
The difference between the natural frequency and the external frequency determines the magnitude of forced oscillations.
The system’s damping capacity.
The external force’s strength.