Angular Velocity of Vibration using Force Transmitted Calculator

✖Force Transmitted is the amount of energy transferred from a vibrating system to another system or structure, affecting its motion and stability.ⓘ Force Transmitted [F_T]			+10% -10%
✖Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.ⓘ Maximum Displacement [K]			+10% -10%
✖Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.ⓘ Stiffness of Spring [k]			+10% -10%
✖Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.ⓘ Damping Coefficient [c]			+10% -10%

✖Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.ⓘ Angular Velocity of Vibration using Force Transmitted [ω]

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Angular Velocity of Vibration using Force Transmitted Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Angular Velocity - (Measured in Radian per Second) - Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.
Force Transmitted - (Measured in Newton) - Force Transmitted is the amount of energy transferred from a vibrating system to another system or structure, affecting its motion and stability.
Maximum Displacement - (Measured in Meter) - Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.

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
Damping Coefficient: 9000.022 Newton Second per Meter --> 9000.022 Newton Second per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω = (sqrt((F_T/K)^2-k^2))/c --> (sqrt((48021.6/0.8)^2-60000^2))/9000.022

Evaluating ... ...

ω = 0.200022009791797

STEP 3: Convert Result to Output's Unit

0.200022009791797 Radian per Second --> No Conversion Required

FINAL ANSWER

0.200022009791797 ≈ 0.200022 Radian per Second <-- Angular Velocity

(Calculation completed in 00.004 seconds)

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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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< Vibration Isolation and Transmissibility Calculators

Maximum Displacement of Vibration using Force Transmitted

LaTeX Go Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))

Stiffness of Spring using Force Transmitted

LaTeX Go Stiffness of Spring = sqrt((Force Transmitted/Maximum Displacement)^2-(Damping Coefficient*Angular Velocity)^2)

Damping Coefficient using Force Transmitted

LaTeX Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity

Force Transmitted

LaTeX Go Force Transmitted = Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)

< Forced Vibration Calculators

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

LaTeX Go Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio

Angular Velocity of Vibration using Force Transmitted

LaTeX Go Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient

Damping Coefficient using Force Transmitted

LaTeX Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity

Applied Force given Transmissibility Ratio

LaTeX Go Applied Force = Force Transmitted/Transmissibility Ratio

Angular Velocity of Vibration using Force Transmitted Formula

LaTeX Go

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

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 Angular Velocity of Vibration using Force Transmitted?

Angular Velocity of Vibration using Force Transmitted calculator uses Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient to calculate the Angular Velocity, Angular Velocity of Vibration using Force Transmitted formula is defined as a measure of the rotational speed of an object vibrating due to an external force, providing insight into the oscillatory motion of the object in a mechanical system. Angular Velocity is denoted by ω symbol.

How to calculate Angular Velocity of Vibration using Force Transmitted using this online calculator? To use this online calculator for Angular Velocity of Vibration using Force Transmitted, enter Force Transmitted (F_T), Maximum Displacement (K), Stiffness of Spring (k) & Damping Coefficient (c) and hit the calculate button. Here is how the Angular Velocity of Vibration using Force Transmitted calculation can be explained with given input values -> 0.200022 = (sqrt((48021.6/0.8)^2-60000^2))/9000.022.

FAQ

What is Angular Velocity of Vibration using Force Transmitted?

Angular Velocity of Vibration using Force Transmitted formula is defined as a measure of the rotational speed of an object vibrating due to an external force, providing insight into the oscillatory motion of the object in a mechanical system and is represented as ω = (sqrt((F_T/K)^2-k^2))/c or Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient. Force Transmitted is the amount of energy transferred from a vibrating system to another system or structure, affecting its motion and stability, Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system, Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched & Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.

How to calculate Angular Velocity of Vibration using Force Transmitted?

Angular Velocity of Vibration using Force Transmitted formula is defined as a measure of the rotational speed of an object vibrating due to an external force, providing insight into the oscillatory motion of the object in a mechanical system is calculated using Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient. To calculate Angular Velocity of Vibration using Force Transmitted, you need Force Transmitted (F_T), Maximum Displacement (K), Stiffness of Spring (k) & Damping Coefficient (c). With our tool, you need to enter the respective value for Force Transmitted, Maximum Displacement, Stiffness of Spring & Damping Coefficient 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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