Maximum Displacement of Forced Vibration at Resonance Calculator

✖Deflection under static force refers to the displacement or deformation of a structure or object when subjected to a constant, unchanging force.ⓘ Deflection under Static Force [x_o]			+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%
✖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%
✖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 at Resonance [d_max]

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Formula

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Maximum Displacement of Forced Vibration at Resonance

Formula

d max = x o \cdot \frac{k}{c \cdot ω n}

Example

0.56101 m = 0.3333333 m \cdot \frac{60 N/m}{5 Ns/m \cdot 7.13 rad/s}

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Maximum Displacement of Forced Vibration at Resonance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
d_max = x_o*k/(c*ω_n)
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.
Deflection under Static Force - (Measured in Meter) - Deflection under static force refers to the displacement or deformation of a structure or object when subjected to a constant, unchanging force.
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.
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.
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 under Static Force: 0.3333333 Meter --> 0.3333333 Meter No Conversion Required
Stiffness of Spring: 60 Newton per Meter --> 60 Newton per Meter No Conversion Required
Damping Coefficient: 5 Newton Second per Meter --> 5 Newton Second 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_o*k/(c*ω_n) --> 0.3333333*60/(5*7.13)

Evaluating ... ...

d_max = 0.561009761570828

STEP 3: Convert Result to Output's Unit

0.561009761570828 Meter --> No Conversion Required

FINAL ANSWER

0.561009761570828 ≈ 0.56101 Meter <-- Maximum Displacement

(Calculation completed in 00.004 seconds)

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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

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

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

Deflection of System under Static Force

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

Static Force

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

Maximum Displacement of Forced Vibration at Resonance Formula

Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
d_max = x_o*k/(c*ω_n)

What is Overdamped Free Vibration?

Overdamped free vibration occurs in a system where the damping is so strong that it prevents the system from oscillating. In this case, when the system is disturbed from its equilibrium position, it returns to equilibrium without undergoing any oscillatory motion. The return to equilibrium happens slowly, and the system may take a longer time to settle compared to underdamped vibrations. Overdamping is typically observed in systems with high resistance, such as heavy damping materials or mechanisms designed to reduce vibrations.

How to Calculate Maximum Displacement of Forced Vibration at Resonance?

Maximum Displacement of Forced Vibration at Resonance calculator uses Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency) to calculate the Maximum Displacement, Maximum Displacement of Forced Vibration at Resonance formula is defined as the maximum amplitude of oscillation that occurs in a vibrating system when the frequency of the external force matches the natural frequency of the system, resulting in the largest possible displacement. Maximum Displacement is denoted by d_max symbol.

How to calculate Maximum Displacement of Forced Vibration at Resonance using this online calculator? To use this online calculator for Maximum Displacement of Forced Vibration at Resonance, enter Deflection under Static Force (x_o), Stiffness of Spring (k), Damping Coefficient (c) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Maximum Displacement of Forced Vibration at Resonance calculation can be explained with given input values -> 0.258198 = 0.3333333*60/(5*7.13).

FAQ

What is Maximum Displacement of Forced Vibration at Resonance?

Maximum Displacement of Forced Vibration at Resonance formula is defined as the maximum amplitude of oscillation that occurs in a vibrating system when the frequency of the external force matches the natural frequency of the system, resulting in the largest possible displacement and is represented as d_max = x_o*k/(c*ω_n) or Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency). Deflection under static force refers to the displacement or deformation of a structure or object when subjected to a constant, unchanging force, 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, Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force & 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 at Resonance?

Maximum Displacement of Forced Vibration at Resonance formula is defined as the maximum amplitude of oscillation that occurs in a vibrating system when the frequency of the external force matches the natural frequency of the system, resulting in the largest possible displacement is calculated using Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency). To calculate Maximum Displacement of Forced Vibration at Resonance, you need Deflection under Static Force (x_o), Stiffness of Spring (k), Damping Coefficient (c) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Deflection under Static Force, Stiffness of Spring, Damping Coefficient & 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 under Static Force, Stiffness of Spring, Damping Coefficient & Natural Circular Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)
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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