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Periodic Time of Vibration using Natural Frequency Formula

GoPeriodic Time of Vibration 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{{ω n}^{2} - a^{2}}}

t_p - Time Period?ω_n - Natural Circular Frequency?a - Frequency Constant for Calculation?π - Archimedes' constant?

Periodic Time of Vibration using Natural Frequency Example

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

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

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

0.2992 = \frac{2 \cdot 3.1416}{\sqrt{21^{2} - {0.2}^{2}}}

0.2992s = \frac{2 \cdot 3.1416}{\sqrt{{21rad/s}^{2} - {0.2Hz}^{2}}}

0.2992 = \frac{2 \cdot 3.1416}{\sqrt{21^{2} - {0.2}^{2}}}

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Periodic Time of Vibration using Natural Frequency Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

t p = \frac{2 \cdot π}{\sqrt{{21rad/s}^{2} - {0.2Hz}^{2}}}

Next Step Substitute values of Constants

∴

t p = \frac{2 \cdot 3.1416}{\sqrt{{21rad/s}^{2} - {0.2Hz}^{2}}}

Next Step Prepare to Evaluate

∴

t p = \frac{2 \cdot 3.1416}{\sqrt{21^{2} - {0.2}^{2}}}

Next Step Evaluate

∴

t p = 0.299212870394292s

LAST Step Rounding Answer

∴

t p = 0.2992s

Periodic Time of Vibration using Natural Frequency 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

Natural Circular Frequency

Natural Circular Frequency is a scalar measure of rotation rate.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular Frequency

Frequency Constant for Calculation

The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.

Symbol: a

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Frequency Constant for Calculation

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

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

Periodic Time of Vibration using Natural Frequency evaluator uses Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)) to evaluate the Time Period, Periodic Time of Vibration using Natural Frequency formula is defined as the time taken by an object to complete one oscillation in a free damped vibration, which is influenced by the natural frequency and damping force, and is a crucial parameter in understanding the behavior of vibrating systems in various fields such as physics and engineering. Time Period is denoted by t_p symbol.

How to evaluate Periodic Time of Vibration using Natural Frequency using this online evaluator? To use this online evaluator for Periodic Time of Vibration using Natural Frequency, enter Natural Circular Frequency (ω_n) & Frequency Constant for Calculation (a) and hit the calculate button.

FAQs on Periodic Time of Vibration using Natural Frequency

What is the formula to find Periodic Time of Vibration using Natural Frequency?

The formula of Periodic Time of Vibration using Natural Frequency is expressed as Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)). Here is an example- 0.299213 = (2*pi)/(sqrt(21^2-0.2^2)).

How to calculate Periodic Time of Vibration using Natural Frequency?

With Natural Circular Frequency (ω_n) & Frequency Constant for Calculation (a) we can find Periodic Time of Vibration using Natural Frequency using the formula - Time Period = (2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)). This formula also uses Archimedes' constant and Square Root (sqrt) 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(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2))

Can the Periodic Time of Vibration using Natural Frequency be negative?

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

Which unit is used to measure Periodic Time of Vibration using Natural Frequency?

Periodic Time of Vibration using Natural Frequency 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 using Natural Frequency can be measured.

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