# Critical Damping Applications:Detailed insights

Critical damping applications are one of the primary forms of bringing an oscillating system to rest. Essential plates of damping are used to get the vibrations of the system to complete rest.

Given below are a few critical damping applications that are found in daily life. Critical damping are very useful for such daily-life activities.

## Friction Damping Plates

Friction damping plates are the devices that reduce the excessive vibrations in a system, thus converting kinetic energy into thermal energy through friction. The concept of critical damping comes into action here.

This brings the massive vibrations to the equilibrium position as quickly as possible. Therefore the friction damping plates are primarily used in building to dissipate seismic energy by which the building can withstand an earthquake.

The concept is, when a building encounters an earthquake, the plates underground change places but the friction damping plates make sure plates under the construction come back to the rest position, causing less destruction. In this way, critical damping applications find their uses.

## Electric Circuit Damping

A primary RLC circuit is known as an electrical circuit. R means resistor, L means inductor, and C implies capacitor.

In this circuit, an inductor (L) stores the energy in a magnetic field when the electric current flows through the circuit; a capacitor (C) stores electric charges, which is why the electric current passes. But a resistor (R) breaks the current flow in a system similar to the damping in oscillating systems.

Here the addition of a resistor in an electric circuit decays the oscillations of the circuit when connected in parallel.

The resistor reduces the peak resonant frequency in the circuit. Critical damping is one of the primary reasons for reducing frequency due to the arising from the LC combination in the RLC circuit.

## Hydraulic Recoil Mechanism

When a firearm fitted with hydraulic recoil, it reduces the effects of recoil in the gun and provides accuracy. The hydraulic recoil fixed in the barrel, so when the gun is fired, the recoil energy caused by the projectile makes the barrel go backward and locked in the bolt.

Basically, a barrel and the bold are together, soon after firing next step is that the barrel and bold travel backward till the end of the gun and come forward with some force so that the bold is firm, filling the next cartridge. In contrast, the barrel goes forwards and pushes the current cartridge to be fired.

This phenomenon occurs because the critical damping is present; this helps the barrel return to the rest position as quickly as possible to fire the next one.

## Door-closing Mechanism

Adding a door damper (critically damped) reduces the damage to the door system as a whole.

Generally, when a door opens and closes, it makes noise, and damage occurs to the doorframe and such. So when a damper attaches to the door, it reduces the door from slamming and causing destruction.

Once the door opens, it suddenly comes back to its original position with no further delay and also has no adverse effect on the system. Critical damping helps the system from further damage or so.

## Speedometer

Speedometers are critically damped instruments so that when the vehicle accelerates, it does not oscillate and create disturbances during riding or driving.

In the speedometer, the needle that indicates the speed does not constantly oscillate and confuses the person handling the vehicle.

Since the speedometer is critically damped, it does not have a constant oscillation; once the vehicle is accelerated, it does not oscillate at all and stays in that stable position unless the velocity is changed, which changes the acceleration.

## Automobile Shock Absorber

Shock absorbers are a spring present in cars that dissipate the energy created from an abrupt movement while the car goes through a rough patch. This spring smoothens the entire ride of the vehicle.

The spring, also called a shock absorber, absorbs part of the abrupt movement in the form of energy during the ride, which dissipates the energy.

As this is a continuous process, the spring has to do this as quickly as possible, so the car goes up and down. The shock absorber returns to its original place and controls the process as well.

## What is critical damping resistance

Critical damping resistance is the resistance of a critically damped electric circuit and ceases the oscillations.

An RLC circuit is the best suited to determine the resistance of a critically damped circuit. R is the resistor, L is the inductor, and C is the capacitor. The LC combination is the reason behind the oscillations of the system. R-value affects the damping of the whole system.

When R is small or large, it means the circuit is either underdamped or overdamped. When the circuit is underdamped, ringing happens that is the function of the circuit occurs. Here it is ringing, but in the other circuits, it can be ringing and any other application.

When R is made small, it reduces the frequency due to the oscillation in the system. Resistance is the one that breaks the flow of electric current, hence in a circuit, the resistance and cuts down the peaks of the resonant frequency.

The critical damping resistance can also be explained as the required resistance to stop the oscillations and bring them back to the equilibrium position.

## How to find critical damping resistance

Critical damping resistance is calculated using the damping factor. This formula is used to find the critical damping resistance.

For a critically damped circuit(R LC in parallel), the resistance can be found using the formula:   ζ = R/2 (C/L)1/2 .  Zeta (ζ) is the damping factor and for critical damping (ζ) is 1.

Let us understand using a numerical problem. Calculate the critical damping resistance in the given circuit.

ζ = R/2 (C/L)1/2

1= R/2 (64/16)1/2

1= R/2 x 4

R = 0.5 Ω

## Critical damping condition

The condition for the critical damping is that the damping factor should be equal to 1. That is Zeta (ζ) = 1.

In a system, the oscillations will completely decay; that is, it will stop and come back to the rest state, the equilibrium position, called critical damping.

The minimum amount of force or resistance (based on which system we are working on) required to stop the system under motion to bring it back to the equilibrium system is critical damping.

The condition for a critically damped system directly depends on the damping factor.  And the requirement for critical damping is that the damping factor should always be equal to 1.

The one primary condition for critical damping is that the oscillations must come to a stop without going back and forth and returning to the equilibrium position as quickly as possible.