Natural Circular Frequency given Displacement of Body Calculator

✖Time Period is the duration between two consecutive oscillations of a freely vibrating object in the longitudinal direction, characterizing its natural frequency.ⓘ Time Period [t_p]

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✖Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.ⓘ Natural Circular Frequency given Displacement of Body [ω_n]

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Natural Circular Frequency given Displacement of Body Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Circular Frequency = (2*pi)/Time Period
ω_n = (2*pi)/t_p
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.
Time Period - (Measured in Second) - Time Period is the duration between two consecutive oscillations of a freely vibrating object in the longitudinal direction, characterizing its natural frequency.

STEP 1: Convert Input(s) to Base Unit

Time Period: 0.299136 Second --> 0.299136 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_n = (2*pi)/t_p --> (2*pi)/0.299136

Evaluating ... ...

ω_n = 21.0044438221397

STEP 3: Convert Result to Output's Unit

21.0044438221397 Radian per Second --> No Conversion Required

FINAL ANSWER

21.0044438221397 ≈ 21.00444 Radian per Second <-- Natural Circular Frequency

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Rayleigh’s Method Calculators

Velocity at Mean Position

LaTeX Go Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken)

Maximum Kinetic Energy at Mean Position

LaTeX Go Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2

Maximum Potential Energy at Mean Position

LaTeX Go Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2

Maximum Velocity at Mean Position by Rayleigh Method

LaTeX Go Maximum Velocity = Natural Circular Frequency*Maximum Displacement

Natural Circular Frequency given Displacement of Body Formula

LaTeX Go

Natural Circular Frequency = (2*pi)/Time Period
ω_n = (2*pi)/t_p

What is Rayleigh's method in vibration analysis?

The Rayleigh's quotient represents a quick method to estimate the natural frequency of a multi-degree-of-freedom vibration system, in which the mass and the stiffness matrices are known.

How to Calculate Natural Circular Frequency given Displacement of Body?

Natural Circular Frequency given Displacement of Body calculator uses Natural Circular Frequency = (2*pi)/Time Period to calculate the Natural Circular Frequency, Natural Circular Frequency given Displacement of Body formula is defined as a measure of the number of oscillations or cycles per unit time of a body in free longitudinal vibrations, which helps in understanding the vibrational characteristics of the body. Natural Circular Frequency is denoted by ω_n symbol.

How to calculate Natural Circular Frequency given Displacement of Body using this online calculator? To use this online calculator for Natural Circular Frequency given Displacement of Body, enter Time Period (t_p) and hit the calculate button. Here is how the Natural Circular Frequency given Displacement of Body calculation can be explained with given input values -> 21.00444 = (2*pi)/0.299136.

FAQ

What is Natural Circular Frequency given Displacement of Body?

Natural Circular Frequency given Displacement of Body formula is defined as a measure of the number of oscillations or cycles per unit time of a body in free longitudinal vibrations, which helps in understanding the vibrational characteristics of the body and is represented as ω_n = (2*pi)/t_p or Natural Circular Frequency = (2*pi)/Time Period. Time Period is the duration between two consecutive oscillations of a freely vibrating object in the longitudinal direction, characterizing its natural frequency.

How to calculate Natural Circular Frequency given Displacement of Body?

Natural Circular Frequency given Displacement of Body formula is defined as a measure of the number of oscillations or cycles per unit time of a body in free longitudinal vibrations, which helps in understanding the vibrational characteristics of the body is calculated using Natural Circular Frequency = (2*pi)/Time Period. To calculate Natural Circular Frequency given Displacement of Body, you need Time Period (t_p). With our tool, you need to enter the respective value for Time Period 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 Natural Circular Frequency?

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

Natural Circular Frequency = Maximum Velocity/Maximum Displacement

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