Displacement of Mass from Mean Position Calculator

✖Amplitude of Vibration is the greatest distance that a wave, especially a sound or radio wave, moves up and down.ⓘ Amplitude of Vibration [A]			+10% -10%
✖Circular Damped Frequency refers to the angular displacement per unit time.ⓘ Circular Damped Frequency [ω_d]			+10% -10%
✖Time Period is the time taken by a complete cycle of the wave to pass a point.ⓘ Time Period [t_p]			+10% -10%

✖Total Displacement is a vector quantity that represents the change in an object's position from its initial position.ⓘ Displacement of Mass from Mean Position [d_mass]

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Formula

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Displacement of Mass from Mean Position

Formula

`"d"_{"mass"} = "A"*cos("ω"_{"d"}*"t"_{"p"})`

Example

`"6.603167mm"="10mm"*cos("6"*"3s")`

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Download Frequency of Free Damped Vibrations Formulas PDF

Displacement of Mass from Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency*Time Period)
d_mass = A*cos(ω_d*t_p)
This formula uses 1 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Total Displacement - (Measured in Meter) - Total Displacement is a vector quantity that represents the change in an object's position from its initial position.
Amplitude of Vibration - (Measured in Meter) - Amplitude of Vibration is the greatest distance that a wave, especially a sound or radio wave, moves up and down.
Circular Damped Frequency - Circular Damped Frequency refers to the angular displacement per unit time.
Time Period - (Measured in Second) - Time Period is the time taken by a complete cycle of the wave to pass a point.

STEP 1: Convert Input(s) to Base Unit

Amplitude of Vibration: 10 Millimeter --> 0.01 Meter (Check conversion here)
Circular Damped Frequency: 6 --> No Conversion Required
Time Period: 3 Second --> 3 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_mass = A*cos(ω_d*t_p) --> 0.01*cos(6*3)

Evaluating ... ...

d_mass = 0.0066031670824408

STEP 3: Convert Result to Output's Unit

0.0066031670824408 Meter -->6.6031670824408 Millimeter (Check conversion here)

FINAL ANSWER

6.6031670824408 ≈ 6.603167 Millimeter <-- Total Displacement

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Frequency of Free Damped Vibrations » Under Damping » Displacement of Mass from Mean Position

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National Institute Of Technology (NIT), Hamirpur

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< 10+ Under Damping Calculators

Periodic Time of Vibration

Go Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2))

Frequency of Damped Vibration

Go Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)

Circular Damped Frequency

Go Circular Damped Frequency = sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)

Periodic Time of Vibration using Natural Frequency

Go Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2))

Frequency of Damped Vibration using Natural Frequency

Go Frequency = 1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)

Displacement of Mass from Mean Position

Go Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency*Time Period)

Frequency of Undamped Vibration

Go Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring)

Frequency Constant for Damped Vibrations given Circular Frequency

Go Frequency Constant for Calculation = sqrt(Natural Circular Frequency^2-Circular Damped Frequency^2)

Circular Damped Frequency given Natural Frequency

Go Circular Damped Frequency = sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)

Frequency Constant for Damped Vibrations

Go Frequency Constant for Calculation = Damping Coefficient/Mass Suspended from Spring

Displacement of Mass from Mean Position Formula

Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency*Time Period)
d_mass = A*cos(ω_d*t_p)

Why damping happens during vibration?

The mechanical system vibrates at one or more of its natural frequencies and damps down to motionlessness. Damped vibration happens when the energy of a vibrating system is gradually dissipated by friction and other resistances, the vibrations are said to be damped.

How to Calculate Displacement of Mass from Mean Position?

Displacement of Mass from Mean Position calculator uses Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency*Time Period) to calculate the Total Displacement, Displacement of Mass from Mean Position implies that an object has moved, or has been displaced. Total Displacement is denoted by d_mass symbol.

How to calculate Displacement of Mass from Mean Position using this online calculator? To use this online calculator for Displacement of Mass from Mean Position, enter Amplitude of Vibration (A), Circular Damped Frequency (ω_d) & Time Period (t_p) and hit the calculate button. Here is how the Displacement of Mass from Mean Position calculation can be explained with given input values -> 6603.167 = 0.01*cos(6*3).

FAQ

What is Displacement of Mass from Mean Position?

Displacement of Mass from Mean Position implies that an object has moved, or has been displaced and is represented as d_mass = A*cos(ω_d*t_p) or Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency*Time Period). Amplitude of Vibration is the greatest distance that a wave, especially a sound or radio wave, moves up and down, Circular Damped Frequency refers to the angular displacement per unit time & Time Period is the time taken by a complete cycle of the wave to pass a point.

How to calculate Displacement of Mass from Mean Position?

Displacement of Mass from Mean Position implies that an object has moved, or has been displaced is calculated using Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency*Time Period). To calculate Displacement of Mass from Mean Position, you need Amplitude of Vibration (A), Circular Damped Frequency (ω_d) & Time Period (t_p). With our tool, you need to enter the respective value for Amplitude of Vibration, Circular Damped Frequency & Time Period 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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