Maximum Displacement of Forced Vibration with Negligible Damping 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%
✖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%
✖Natural frequency is the frequency at which a system tends to oscillate when not subjected to external forces.ⓘ Natural Frequency [ω_nat]			+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%

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

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Maximum Displacement of Forced Vibration with Negligible Damping Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2))
d_max = F_x/(m*(ω_nat^2-ω^2))
This formula uses 5 Variables

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.
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.
Natural Frequency - (Measured in Radian per Second) - Natural frequency is the frequency at which a system tends to oscillate when not subjected to external forces.
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.

STEP 1: Convert Input(s) to Base Unit

Static Force: 20 Newton --> 20 Newton No Conversion Required
Mass suspended from Spring: 0.25 Kilogram --> 0.25 Kilogram No Conversion Required
Natural Frequency: 15.5757020883064 Radian per Second --> 15.5757020883064 Radian per Second No Conversion Required
Angular Velocity: 10 Radian per Second --> 10 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_max = F_x/(m*(ω_nat^2-ω^2)) --> 20/(0.25*(15.5757020883064^2-10^2))

Evaluating ... ...

d_max = 0.560999999999999

STEP 3: Convert Result to Output's Unit

0.560999999999999 Meter --> No Conversion Required

FINAL ANSWER

0.560999999999999 ≈ 0.561 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 with Negligible Damping

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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 with Negligible Damping Formula

LaTeX Go

Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2))
d_max = F_x/(m*(ω_nat^2-ω^2))

What is Damping?

Damping refers to the reduction of oscillations or vibrations in a mechanical system due to the dissipation of energy. It occurs when energy is lost through mechanisms such as friction, air resistance, or internal material properties. Damping plays a crucial role in controlling the amplitude of vibrations, helping to stabilize systems and prevent excessive oscillations. There are different types of damping, including underdamping, overdamping, and critical damping, each affecting how quickly a system returns to equilibrium after being disturbed.

How to Calculate Maximum Displacement of Forced Vibration with Negligible Damping?

Maximum Displacement of Forced Vibration with Negligible Damping calculator uses Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2)) to calculate the Maximum Displacement, Maximum Displacement of Forced Vibration with Negligible Damping formula is defined as the maximum amplitude of oscillation that occurs in a forced vibration system when the damping force is negligible, providing insight into the system's response to external forces. Maximum Displacement is denoted by d_max symbol.

How to calculate Maximum Displacement of Forced Vibration with Negligible Damping using this online calculator? To use this online calculator for Maximum Displacement of Forced Vibration with Negligible Damping, enter Static Force (F_x), Mass suspended from Spring (m), Natural Frequency (ω_nat) & Angular Velocity (ω) and hit the calculate button. Here is how the Maximum Displacement of Forced Vibration with Negligible Damping calculation can be explained with given input values -> 0.559252 = 20/(0.25*(15.5757020883064^2-10^2)).

FAQ

What is Maximum Displacement of Forced Vibration with Negligible Damping?

Maximum Displacement of Forced Vibration with Negligible Damping formula is defined as the maximum amplitude of oscillation that occurs in a forced vibration system when the damping force is negligible, providing insight into the system's response to external forces and is represented as d_max = F_x/(m*(ω_nat^2-ω^2)) or Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2)). Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations, The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress, Natural frequency is the frequency at which a system tends to oscillate when not subjected to external forces & Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.

How to calculate Maximum Displacement of Forced Vibration with Negligible Damping?

Maximum Displacement of Forced Vibration with Negligible Damping formula is defined as the maximum amplitude of oscillation that occurs in a forced vibration system when the damping force is negligible, providing insight into the system's response to external forces is calculated using Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2)). To calculate Maximum Displacement of Forced Vibration with Negligible Damping, you need Static Force (F_x), Mass suspended from Spring (m), Natural Frequency (ω_nat) & Angular Velocity (ω). With our tool, you need to enter the respective value for Static Force, Mass suspended from Spring, Natural Frequency & Angular Velocity 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, Mass suspended from Spring, Natural Frequency & Angular Velocity. 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 = (Deflection)/(sqrt(((Damping Coefficient^2)*(Angular Velocity^2))/(Stiffness of Spring^2))+(1-((Angular Velocity^2)/(Natural Circular Frequency^2)))^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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