Maximum Displacement of Forced Vibration using Natural Frequency Calculator

✖Deflection refers to the displacement of a structural element or object under load. It measures how much a point moves from its original position due to applied forces.ⓘ Deflection [x]			+10% -10%
✖Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force.ⓘ Damping Coefficient [c]			+10% -10%
✖Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.ⓘ Angular Velocity [ω]			+10% -10%
✖The stiffness of spring is a measure of its resistance to deformation when a force is applied, it quantifies how much the spring compresses or extends in response to a given load.ⓘ Stiffness of Spring [k]			+10% -10%
✖Natural Circular Frequency is the frequency at which a system tends to oscillate in the absence of any external force.ⓘ Natural Circular Frequency [ω_n]			+10% -10%

✖Maximum displacement refers to the largest distance a vibrating system moves from its equilibrium position during oscillation.ⓘ Maximum Displacement of Forced Vibration using Natural Frequency [d_max]

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Maximum Displacement of Forced Vibration using Natural Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = (Deflection)/(sqrt(((Damping Coefficient^2)*(Angular Velocity^2))/(Stiffness of Spring^2))+(1-((Angular Velocity^2)/(Natural Circular Frequency^2)))^2)
d_max = (x)/(sqrt(((c^2)*(ω^2))/(k^2))+(1-((ω^2)/(ω_n^2)))^2)
This formula uses 1 Functions, 6 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

Maximum Displacement - (Measured in Meter) - Maximum displacement refers to the largest distance a vibrating system moves from its equilibrium position during oscillation.
Deflection - (Measured in Meter) - Deflection refers to the displacement of a structural element or object under load. It measures how much a point moves from its original position due to applied forces.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force.
Angular Velocity - (Measured in Radian per Second) - Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.
Stiffness of Spring - (Measured in Newton per Meter) - The stiffness of spring is a measure of its resistance to deformation when a force is applied, it quantifies how much the spring compresses or extends in response to a given load.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the frequency at which a system tends to oscillate in the absence of any external force.

STEP 1: Convert Input(s) to Base Unit

Deflection: 0.993 Meter --> 0.993 Meter No Conversion Required
Damping Coefficient: 5 Newton Second per Meter --> 5 Newton Second per Meter No Conversion Required
Angular Velocity: 10 Radian per Second --> 10 Radian per Second No Conversion Required
Stiffness of Spring: 60 Newton per Meter --> 60 Newton per Meter No Conversion Required
Natural Circular Frequency: 7.13 Radian per Second --> 7.13 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_max = (x)/(sqrt(((c^2)*(ω^2))/(k^2))+(1-((ω^2)/(ω_n^2)))^2) --> (0.993)/(sqrt(((5^2)*(10^2))/(60^2))+(1-((10^2)/(7.13^2)))^2)

Evaluating ... ...

d_max = 0.561471335970737

STEP 3: Convert Result to Output's Unit

0.561471335970737 Meter --> No Conversion Required

FINAL ANSWER

0.561471335970737 ≈ 0.561471 Meter <-- Maximum Displacement

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Frequency of Under Damped Forced Vibrations » Maximum Displacement of Forced Vibration using Natural Frequency

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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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< Frequency of Under Damped Forced Vibrations Calculators

Static Force using Maximum Displacement or Amplitude of Forced Vibration

LaTeX Go Static Force = Maximum Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))

Static Force when Damping is Negligible

LaTeX Go Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2)

Deflection of System under Static Force

LaTeX Go Deflection under Static Force = Static Force/Stiffness of Spring

Static Force

LaTeX Go Static Force = Deflection under Static Force*Stiffness of Spring

Maximum Displacement of Forced Vibration using Natural Frequency Formula

LaTeX Go

What is Displacement?

Displacement refers to the change in position of an object from its initial point to its final point. It is a vector quantity, meaning it has both magnitude and direction. In the context of motion, displacement indicates how far an object has moved and in which direction, regardless of the path taken. It is a crucial concept in physics and engineering, as it helps describe the movement of objects and the effects of forces acting upon them.

How to Calculate Maximum Displacement of Forced Vibration using Natural Frequency?

Maximum Displacement of Forced Vibration using Natural Frequency calculator uses Maximum Displacement = (Deflection)/(sqrt(((Damping Coefficient^2)*(Angular Velocity^2))/(Stiffness of Spring^2))+(1-((Angular Velocity^2)/(Natural Circular Frequency^2)))^2) to calculate the Maximum Displacement, Maximum Displacement of Forced Vibration using Natural Frequency formula is defined as the maximum amplitude of an object's oscillation when subjected to an external force, influenced by the natural frequency of the system, and is a critical parameter in understanding the behavior of underdamped forced vibrations. Maximum Displacement is denoted by d_max symbol.

How to calculate Maximum Displacement of Forced Vibration using Natural Frequency using this online calculator? To use this online calculator for Maximum Displacement of Forced Vibration using Natural Frequency, enter Deflection (x), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Maximum Displacement of Forced Vibration using Natural Frequency calculation can be explained with given input values -> 0.561471 = (0.993)/(sqrt(((5^2)*(10^2))/(60^2))+(1-((10^2)/(7.13^2)))^2).

FAQ

What is Maximum Displacement of Forced Vibration using Natural Frequency?

Maximum Displacement of Forced Vibration using Natural Frequency formula is defined as the maximum amplitude of an object's oscillation when subjected to an external force, influenced by the natural frequency of the system, and is a critical parameter in understanding the behavior of underdamped forced vibrations and is represented as d_max = (x)/(sqrt(((c^2)*(ω^2))/(k^2))+(1-((ω^2)/(ω_n^2)))^2) or Maximum Displacement = (Deflection)/(sqrt(((Damping Coefficient^2)*(Angular Velocity^2))/(Stiffness of Spring^2))+(1-((Angular Velocity^2)/(Natural Circular Frequency^2)))^2). Deflection refers to the displacement of a structural element or object under load. It measures how much a point moves from its original position due to applied forces, Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force, Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis, The stiffness of spring is a measure of its resistance to deformation when a force is applied, it quantifies how much the spring compresses or extends in response to a given load & Natural Circular Frequency is the frequency at which a system tends to oscillate in the absence of any external force.

How to calculate Maximum Displacement of Forced Vibration using Natural Frequency?

Maximum Displacement of Forced Vibration using Natural Frequency formula is defined as the maximum amplitude of an object's oscillation when subjected to an external force, influenced by the natural frequency of the system, and is a critical parameter in understanding the behavior of underdamped forced vibrations is calculated using Maximum Displacement = (Deflection)/(sqrt(((Damping Coefficient^2)*(Angular Velocity^2))/(Stiffness of Spring^2))+(1-((Angular Velocity^2)/(Natural Circular Frequency^2)))^2). To calculate Maximum Displacement of Forced Vibration using Natural Frequency, you need Deflection (x), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Deflection, Damping Coefficient, Angular Velocity, Stiffness of Spring & Natural Circular Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Maximum Displacement?

In this formula, Maximum Displacement uses Deflection, Damping Coefficient, Angular Velocity, Stiffness of Spring & Natural Circular Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2))
Maximum Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))

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