Periodic Time of Vibration using Natural Frequency Calculator

✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%
✖The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.ⓘ Frequency Constant for Calculation [a]			+10% -10%

✖Time Period is the time taken by a complete cycle of the wave to pass a point.ⓘ Periodic Time of Vibration using Natural Frequency [t_p]

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Periodic Time of Vibration using Natural Frequency

Formula

`"t"_{"p"} = (2*pi)/(sqrt("ω"_{"n"}^2-"a"^2))`

Example

`"0.299213s"=(2*pi)/(sqrt(("21rad/s")^2-("0.2Hz")^2))`

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Download Frequency of Free Damped Vibrations Formulas PDF

Periodic Time of Vibration using Natural Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2))
t_p = (2*pi)/(sqrt(ω_n^2-a^2))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Time Period - (Measured in Second) - Time Period is the time taken by a complete cycle of the wave to pass a point.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
Frequency Constant for Calculation - (Measured in Hertz) - The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.

STEP 1: Convert Input(s) to Base Unit

Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required
Frequency Constant for Calculation: 0.2 Hertz --> 0.2 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_p = (2*pi)/(sqrt(ω_n^2-a^2)) --> (2*pi)/(sqrt(21^2-0.2^2))

Evaluating ... ...

t_p = 0.299212870394292

STEP 3: Convert Result to Output's Unit

0.299212870394292 Second --> No Conversion Required

FINAL ANSWER

0.299212870394292 ≈ 0.299213 Second <-- Time Period

(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 » Periodic Time of Vibration using Natural Frequency

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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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

Periodic Time of Vibration using Natural Frequency Formula

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

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 Periodic Time of Vibration using Natural Frequency?

Periodic Time of Vibration using Natural Frequency calculator uses Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)) to calculate the Time Period, Periodic Time of Vibration using Natural Frequency is defined as the time taken by a complete cycle of the wave to pass a point, Frequency is the number of complete cycle of waves passing a point in unit time. Time Period is denoted by t_p symbol.

How to calculate Periodic Time of Vibration using Natural Frequency using this online calculator? To use this online calculator for Periodic Time of Vibration using Natural Frequency, enter Natural Circular Frequency (ω_n) & Frequency Constant for Calculation (a) and hit the calculate button. Here is how the Periodic Time of Vibration using Natural Frequency calculation can be explained with given input values -> 0.299199 = (2*pi)/(sqrt(21^2-0.2^2)).

FAQ

What is Periodic Time of Vibration using Natural Frequency?

Periodic Time of Vibration using Natural Frequency is defined as the time taken by a complete cycle of the wave to pass a point, Frequency is the number of complete cycle of waves passing a point in unit time and is represented as t_p = (2*pi)/(sqrt(ω_n^2-a^2)) or Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)). Natural Circular Frequency is a scalar measure of rotation rate & The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.

How to calculate Periodic Time of Vibration using Natural Frequency?

Periodic Time of Vibration using Natural Frequency is defined as the time taken by a complete cycle of the wave to pass a point, Frequency is the number of complete cycle of waves passing a point in unit time is calculated using Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)). To calculate Periodic Time of Vibration using Natural Frequency, you need Natural Circular Frequency (ω_n) & Frequency Constant for Calculation (a). With our tool, you need to enter the respective value for Natural Circular Frequency & Frequency Constant for Calculation 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 Time Period?

In this formula, Time Period uses Natural Circular Frequency & Frequency Constant for Calculation. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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