Displacement of Mass from Mean Position Calculator

✖Amplitude Vibration is the greatest distance that a wave, especially a sound or radio wave, moves up and down.ⓘ Amplitude 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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Displacement of Mass from Mean Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Displacement = Amplitude 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 Vibration - (Measured in Meter) - Amplitude 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 Vibration: 10 Millimeter --> 0.01 Meter (Check conversion here)
Circular Damped Frequency: 6 --> No Conversion Required
Time Period: 0.9 Second --> 0.9 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*0.9)

Evaluating ... ...

d_mass = 0.00634692875942635

STEP 3: Convert Result to Output's Unit

0.00634692875942635 Meter -->6.34692875942635 Millimeter (Check conversion here)

FINAL ANSWER

6.34692875942635 ≈ 6.346929 Millimeter <-- Total Displacement

(Calculation completed in 00.004 seconds)

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

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National Institute Of Technology (NIT), Hamirpur

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< Frequency of Free Damped Vibrations Calculators

Condition for Critical Damping

LaTeX Go Critical Damping Coefficient = 2*Mass Suspended from Spring*sqrt(Stiffness of Spring/Mass Suspended from Spring)

Damping Factor given Natural Frequency

LaTeX Go Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency)

Critical Damping Coefficient

LaTeX Go Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency

Damping Factor

LaTeX Go Damping Ratio = Damping Coefficient/Critical Damping Coefficient

Displacement of Mass from Mean Position Formula

LaTeX Go

Total Displacement = Amplitude 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 Vibration*cos(Circular Damped Frequency*Time Period) to calculate the Total Displacement, Displacement of Mass from Mean Position formula is defined as a measure of the distance of an object from its mean position in a vibrational motion, describing the oscillatory behavior of an object in a damped vibration system, providing insight into the frequency of free damped vibrations. 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 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*0.9).

FAQ

What is Displacement of Mass from Mean Position?

Displacement of Mass from Mean Position formula is defined as a measure of the distance of an object from its mean position in a vibrational motion, describing the oscillatory behavior of an object in a damped vibration system, providing insight into the frequency of free damped vibrations and is represented as d_mass = A*cos(ω_d*t_p) or Total Displacement = Amplitude Vibration*cos(Circular Damped Frequency*Time Period). Amplitude 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 formula is defined as a measure of the distance of an object from its mean position in a vibrational motion, describing the oscillatory behavior of an object in a damped vibration system, providing insight into the frequency of free damped vibrations is calculated using Total Displacement = Amplitude Vibration*cos(Circular Damped Frequency*Time Period). To calculate Displacement of Mass from Mean Position, you need Amplitude Vibration (A), Circular Damped Frequency (ω_d) & Time Period (t_p). With our tool, you need to enter the respective value for Amplitude 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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