Periodic Time of Vibration Calculator

✖Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.ⓘ Stiffness of Spring [k]			+10% -10%
✖A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.ⓘ Mass Suspended from Spring [m]			+10% -10%
✖Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.ⓘ Damping Coefficient [c]			+10% -10%

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

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Periodic Time of Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2))
t_p = (2*pi)/(sqrt(k/m-(c/(2*m))^2))
This formula uses 1 Constants, 1 Functions, 4 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.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.
Mass Suspended from Spring - (Measured in Kilogram) - A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Spring: 60 Newton per Meter --> 60 Newton per Meter No Conversion Required
Mass Suspended from Spring: 1.25 Kilogram --> 1.25 Kilogram No Conversion Required
Damping Coefficient: 0.8 Newton Second per Meter --> 0.8 Newton Second per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_p = (2*pi)/(sqrt(k/m-(c/(2*m))^2)) --> (2*pi)/(sqrt(60/1.25-(0.8/(2*1.25))^2))

Evaluating ... ...

t_p = 0.907868592310238

STEP 3: Convert Result to Output's Unit

0.907868592310238 Second --> No Conversion Required

FINAL ANSWER

0.907868592310238 ≈ 0.907869 Second <-- Time Period

(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 » Periodic Time of Vibration

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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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< 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

Periodic Time of Vibration Formula

LaTeX Go

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

Periodic Time of Vibration calculator uses Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)) to calculate the Time Period, Periodic Time of Vibration formula is defined as the time required for one complete oscillation or cycle of free damped vibration, which is a fundamental concept in physics and engineering, characterizing the repetitive motion of an object under the influence of a restoring force. Time Period is denoted by t_p symbol.

How to calculate Periodic Time of Vibration using this online calculator? To use this online calculator for Periodic Time of Vibration, enter Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c) and hit the calculate button. Here is how the Periodic Time of Vibration calculation can be explained with given input values -> 0.907869 = (2*pi)/(sqrt(60/1.25-(0.8/(2*1.25))^2)).

FAQ

What is Periodic Time of Vibration?

Periodic Time of Vibration formula is defined as the time required for one complete oscillation or cycle of free damped vibration, which is a fundamental concept in physics and engineering, characterizing the repetitive motion of an object under the influence of a restoring force and is represented as t_p = (2*pi)/(sqrt(k/m-(c/(2*m))^2)) or Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)). Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness, A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter & Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.

How to calculate Periodic Time of Vibration?

Periodic Time of Vibration formula is defined as the time required for one complete oscillation or cycle of free damped vibration, which is a fundamental concept in physics and engineering, characterizing the repetitive motion of an object under the influence of a restoring force is calculated using Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)). To calculate Periodic Time of Vibration, you need Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c). With our tool, you need to enter the respective value for Stiffness of Spring, Mass Suspended from Spring & Damping Coefficient 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 Stiffness of Spring, Mass Suspended from Spring & Damping Coefficient. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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