Maximum Displacement of Forced Vibration Calculator

✖Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations.ⓘ Static Force [F_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%
✖The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.ⓘ Mass suspended from Spring [m]			+10% -10%

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

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Maximum Displacement of Forced Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
d_max = F_x/(sqrt((c*ω)^2-(k-m*ω^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.
Static Force - (Measured in Newton) - Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations.
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.
Mass suspended from Spring - (Measured in Kilogram) - The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.

STEP 1: Convert Input(s) to Base Unit

Static Force: 20 Newton --> 20 Newton 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
Mass suspended from Spring: 0.25 Kilogram --> 0.25 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_max = F_x/(sqrt((c*ω)^2-(k-m*ω^2)^2)) --> 20/(sqrt((5*10)^2-(60-0.25*10^2)^2))

Evaluating ... ...

d_max = 0.560112033611204

STEP 3: Convert Result to Output's Unit

0.560112033611204 Meter --> No Conversion Required

FINAL ANSWER

0.560112033611204 ≈ 0.560112 Meter <-- Maximum Displacement

(Calculation completed in 00.004 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

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National Institute Of Technology (NIT), Hamirpur

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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 Formula

LaTeX Go

Maximum Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
d_max = F_x/(sqrt((c*ω)^2-(k-m*ω^2)^2))

What is Under Damped Free Vibration?

Under damped free vibration refers to a type of oscillation in which a system experiences some resistance or damping but still oscillates with a gradually decreasing amplitude. In this case, the system vibrates at its natural frequency, but the energy is lost over time due to factors like friction or air resistance. The result is that the oscillations decrease in magnitude while still maintaining a recognizable periodic motion. This behavior is common in many mechanical and structural systems, where some damping is present but not enough to completely suppress the oscillations.

How to Calculate Maximum Displacement of Forced Vibration?

Maximum Displacement of Forced Vibration calculator uses Maximum Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)) to calculate the Maximum Displacement, Maximum Displacement of Forced Vibration formula is defined as a measure of the maximum amplitude of an object's oscillation when subjected to an external force, providing insight into the system's response to periodic forces in underdamped systems, commonly observed in mechanical and structural systems. Maximum Displacement is denoted by d_max symbol.

How to calculate Maximum Displacement of Forced Vibration using this online calculator? To use this online calculator for Maximum Displacement of Forced Vibration, enter Static Force (F_x), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m) and hit the calculate button. Here is how the Maximum Displacement of Forced Vibration calculation can be explained with given input values -> 0.560112 = 20/(sqrt((5*10)^2-(60-0.25*10^2)^2)).

FAQ

What is Maximum Displacement of Forced Vibration?

Maximum Displacement of Forced Vibration formula is defined as a measure of the maximum amplitude of an object's oscillation when subjected to an external force, providing insight into the system's response to periodic forces in underdamped systems, commonly observed in mechanical and structural systems and is represented as d_max = F_x/(sqrt((c*ω)^2-(k-m*ω^2)^2)) or Maximum Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)). Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations, 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 & The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.

How to calculate Maximum Displacement of Forced Vibration?

Maximum Displacement of Forced Vibration formula is defined as a measure of the maximum amplitude of an object's oscillation when subjected to an external force, providing insight into the system's response to periodic forces in underdamped systems, commonly observed in mechanical and structural systems is calculated using Maximum Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)). To calculate Maximum Displacement of Forced Vibration, you need Static Force (F_x), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m). With our tool, you need to enter the respective value for Static Force, Damping Coefficient, Angular Velocity, Stiffness of Spring & Mass suspended from Spring 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 Static Force, Damping Coefficient, Angular Velocity, Stiffness of Spring & Mass suspended from Spring. 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 = (Deflection)/(sqrt(((Damping Coefficient^2)*(Angular Velocity^2))/(Stiffness of Spring^2))+(1-((Angular Velocity^2)/(Natural Circular Frequency^2)))^2)

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