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Periodic Time of Vibration Formula

GoPeriodic Time of Vibration using Natural Frequency Formula

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Time Period is the time taken by a complete cycle of the wave to pass a point. Check FAQs

t p = \frac{2 \cdot π}{\sqrt{\frac{k}{m} - {(\frac{c}{2 \cdot m})}^{2}}}

t_p - Time Period?k - Stiffness of Spring?m - Mass Suspended from Spring?c - Damping Coefficient?π - Archimedes' constant?

Periodic Time of Vibration Example

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Here is how the Periodic Time of Vibration equation looks like with Values.

Here is how the Periodic Time of Vibration equation looks like with Units.

Here is how the Periodic Time of Vibration equation looks like.

0.9079 = \frac{2 \cdot 3.1416}{\sqrt{\frac{60}{1.25} - {(\frac{0.8}{2 \cdot 1.25})}^{2}}}

0.9079s = \frac{2 \cdot 3.1416}{\sqrt{\frac{60N/m}{1.25kg} - {(\frac{0.8Ns/m}{2 \cdot 1.25kg})}^{2}}}

0.9079 = \frac{2 \cdot 3.1416}{\sqrt{\frac{60}{1.25} - {(\frac{0.8}{2 \cdot 1.25})}^{2}}}

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Periodic Time of Vibration Solution

Follow our step by step solution on how to calculate Periodic Time of Vibration?

FIRST Step Consider the formula

t p = \frac{2 \cdot π}{\sqrt{\frac{k}{m} - {(\frac{c}{2 \cdot m})}^{2}}}

Next Step Substitute values of Variables

∴

t p = \frac{2 \cdot π}{\sqrt{\frac{60N/m}{1.25kg} - {(\frac{0.8Ns/m}{2 \cdot 1.25kg})}^{2}}}

Next Step Substitute values of Constants

∴

t p = \frac{2 \cdot 3.1416}{\sqrt{\frac{60N/m}{1.25kg} - {(\frac{0.8Ns/m}{2 \cdot 1.25kg})}^{2}}}

Next Step Prepare to Evaluate

∴

t p = \frac{2 \cdot 3.1416}{\sqrt{\frac{60}{1.25} - {(\frac{0.8}{2 \cdot 1.25})}^{2}}}

Next Step Evaluate

∴

t p = 0.907868592310238s

LAST Step Rounding Answer

∴

t p = 0.9079s

Periodic Time of Vibration Formula Elements

Variables

Constants

Functions

Time Period

Time Period is the time taken by a complete cycle of the wave to pass a point.

Symbol: t_p

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period

Stiffness of Spring

Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.

Symbol: k

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Spring

Mass Suspended from Spring

A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass Suspended from Spring

Damping Coefficient

Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.

Symbol: c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value can be positive or negative.

Formulas to find Damping Coefficient

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Time Period

Go Periodic Time of Vibration using Natural Frequency

t p = \frac{2 \cdot π}{\sqrt{{ω n}^{2} - a^{2}}}

Other formulas in Frequency of Free Damped Vibrations category

Go Condition for Critical Damping

c c = 2 \cdot m \cdot \sqrt{\frac{k}{m}}

Go Critical Damping Coefficient

c c = 2 \cdot m \cdot ω n

Go Damping Factor

ζ = \frac{c}{c c}

Go Damping Factor given Natural Frequency

ζ = \frac{c}{2 \cdot m \cdot ω n}

How to Evaluate Periodic Time of Vibration?

Periodic Time of Vibration evaluator uses Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)) to evaluate 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 evaluate Periodic Time of Vibration using this online evaluator? To use this online evaluator for Periodic Time of Vibration, enter Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c) and hit the calculate button.

FAQs on Periodic Time of Vibration

What is the formula to find Periodic Time of Vibration?

The formula of Periodic Time of Vibration is expressed as Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)). Here is an example- 0.907869 = (2*pi)/(sqrt(60/1.25-(0.8/(2*1.25))^2)).

How to calculate Periodic Time of Vibration?

With Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c) we can find Periodic Time of Vibration using the formula - Time Period = (2*pi)/(sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2)). This formula also uses Archimedes' constant and Square Root Function function(s).

What are the other ways to Calculate Time Period?

Here are the different ways to Calculate Time Period-

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

Can the Periodic Time of Vibration be negative?

No, the Periodic Time of Vibration, measured in Time cannot be negative.

Which unit is used to measure Periodic Time of Vibration?

Periodic Time of Vibration is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Periodic Time of Vibration can be measured.

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Periodic Time of Vibration Formula

​GoPeriodic Time of Vibration using Natural Frequency Formula

Periodic Time of Vibration Example

Periodic Time of Vibration Solution

Periodic Time of Vibration Formula Elements

Other Formulas to find Time Period

Other formulas in Frequency of Free Damped Vibrations category

How to Evaluate Periodic Time of Vibration?

FAQs on Periodic Time of Vibration

Variable Name

GoPeriodic Time of Vibration using Natural Frequency Formula