Damping Coefficient using Force Transmitted Solution

STEP 0: Pre-Calculation Summary
Formula Used
Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity
c = (sqrt((FT/K)^2-k^2))/ω
This formula uses 1 Functions, 5 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.
Force Transmitted - (Measured in Newton) - Force Transmitted in a body is basically governed by Newton's laws of conservation of linear and angular momentum.
Maximum Displacement - (Measured in Meter) - Maximum displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
STEP 1: Convert Input(s) to Base Unit
Force Transmitted: 48021.6 Newton --> 48021.6 Newton No Conversion Required
Maximum Displacement: 0.8 Meter --> 0.8 Meter No Conversion Required
Stiffness of Spring: 60000 Newton per Meter --> 60000 Newton per Meter No Conversion Required
Angular Velocity: 0.2 Radian per Second --> 0.2 Radian per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
c = (sqrt((FT/K)^2-k^2))/ω --> (sqrt((48021.6/0.8)^2-60000^2))/0.2
Evaluating ... ...
c = 9001.01244305196
STEP 3: Convert Result to Output's Unit
9001.01244305196 Newton Second per Meter --> No Conversion Required
FINAL ANSWER
9001.01244305196 9001.012 Newton Second per Meter <-- Damping Coefficient
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Indian Institute of Information Technology (IIIT), Guwahati
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18 Vibration Isolation and Transmissibility Calculators

Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient
Go Transmissibility Ratio = (sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)
Magnification Factor given Transmissibility Ratio given Natural Circular Frequency
Go Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))
Transmissibility Ratio given Natural Circular Frequency and Magnification Factor
Go Transmissibility Ratio = Magnification Factor*sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)
Magnification Factor given Transmissibility Ratio
Go Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Transmissibility Ratio given Magnification Factor
Go Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring
Maximum Displacement of Vibration given Transmissibility Ratio
Go Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration
Go Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio
Transmissibility Ratio
Go Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
Maximum Displacement of Vibration using Force Transmitted
Go Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Angular Velocity of Vibration using Force Transmitted
Go Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient
Stiffness of Spring using Force Transmitted
Go Stiffness of Spring = sqrt((Force Transmitted/Maximum Displacement)^2-(Damping Coefficient*Angular Velocity)^2)
Damping Coefficient using Force Transmitted
Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity
Force Transmitted
Go Force Transmitted = Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)
Natural Circular Frequency given Transmissibility Ratio
Go Natural Circular Frequency = Angular Velocity/(sqrt(1+1/Transmissibility Ratio))
Transmissibility Ratio if there is No Damping
Go Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1)
Transmissibility Ratio given Force Transmitted
Go Transmissibility Ratio = Force Transmitted/Applied Force
Transmitted Force given Transmissibility Ratio
Go Force Transmitted = Transmissibility Ratio*Applied Force
Applied Force given Transmissibility Ratio
Go Applied Force = Force Transmitted/Transmissibility Ratio

18 Forced Vibration Calculators

Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient
Go Transmissibility Ratio = (sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)
Magnification Factor given Transmissibility Ratio given Natural Circular Frequency
Go Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))
Transmissibility Ratio given Natural Circular Frequency and Magnification Factor
Go Transmissibility Ratio = Magnification Factor*sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)
Magnification Factor given Transmissibility Ratio
Go Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Transmissibility Ratio given Magnification Factor
Go Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring
Maximum Displacement of Vibration given Transmissibility Ratio
Go Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration
Go Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio
Transmissibility Ratio
Go Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
Maximum Displacement of Vibration using Force Transmitted
Go Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Angular Velocity of Vibration using Force Transmitted
Go Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient
Damping Coefficient using Force Transmitted
Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity
Stiffness of Spring using Force Transmitted
Go Stiffness of Spring = sqrt((Force Transmitted/Maximum Displacement)^2-(Damping Coefficient*Angular Velocity)^2)
Force Transmitted
Go Force Transmitted = Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)
Natural Circular Frequency given Transmissibility Ratio
Go Natural Circular Frequency = Angular Velocity/(sqrt(1+1/Transmissibility Ratio))
Transmissibility Ratio if there is No Damping
Go Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1)
Transmissibility Ratio given Force Transmitted
Go Transmissibility Ratio = Force Transmitted/Applied Force
Transmitted Force given Transmissibility Ratio
Go Force Transmitted = Transmissibility Ratio*Applied Force
Applied Force given Transmissibility Ratio
Go Applied Force = Force Transmitted/Transmissibility Ratio

Damping Coefficient using Force Transmitted Formula

Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity
c = (sqrt((FT/K)^2-k^2))/ω

What is meant by vibration isolation?

Vibration isolation is a commonly used technique for reducing or suppressing unwanted vibrations in structures and machines. With this technique, the device or system of interest is isolated from the source of vibration through insertion of a resilient member or isolator.

How to Calculate Damping Coefficient using Force Transmitted?

Damping Coefficient using Force Transmitted calculator uses Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity to calculate the Damping Coefficient, The Damping Coefficient using Force Transmitted formula is defined as a material property that indicates whether a material will bounce back or return energy to a system. Damping Coefficient is denoted by c symbol.

How to calculate Damping Coefficient using Force Transmitted using this online calculator? To use this online calculator for Damping Coefficient using Force Transmitted, enter Force Transmitted (FT), Maximum Displacement (K), Stiffness of Spring (k) & Angular Velocity (ω) and hit the calculate button. Here is how the Damping Coefficient using Force Transmitted calculation can be explained with given input values -> 9001.012 = (sqrt((48021.6/0.8)^2-60000^2))/0.2.

FAQ

What is Damping Coefficient using Force Transmitted?
The Damping Coefficient using Force Transmitted formula is defined as a material property that indicates whether a material will bounce back or return energy to a system and is represented as c = (sqrt((FT/K)^2-k^2))/ω or Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity. Force Transmitted in a body is basically governed by Newton's laws of conservation of linear and angular momentum, Maximum displacement implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object, Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness & The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
How to calculate Damping Coefficient using Force Transmitted?
The Damping Coefficient using Force Transmitted formula is defined as a material property that indicates whether a material will bounce back or return energy to a system is calculated using Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity. To calculate Damping Coefficient using Force Transmitted, you need Force Transmitted (FT), Maximum Displacement (K), Stiffness of Spring (k) & Angular Velocity (ω). With our tool, you need to enter the respective value for Force Transmitted, Maximum Displacement, Stiffness of Spring & Angular Velocity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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