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Time Period for Vibrations Formula

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Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system. Check FAQs

t p = 2 \cdot π \cdot \sqrt{\frac{I d}{q}}

t_p - Time Period?I_d - Mass Moment of Inertia of Disc?q - Torsional Stiffness?π - Archimedes' constant?

Time Period for Vibrations Example

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Here is how the Time Period for Vibrations equation looks like with Values.

Here is how the Time Period for Vibrations equation looks like with Units.

Here is how the Time Period for Vibrations equation looks like.

6.7325 = 2 \cdot 3.1416 \cdot \sqrt{\frac{6.2}{5.4}}

6.7325s = 2 \cdot 3.1416 \cdot \sqrt{\frac{6.2kg·m²}{5.4N/m}}

6.7325 = 2 \cdot 3.1416 \cdot \sqrt{\frac{6.2}{5.4}}

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Time Period for Vibrations Solution

Follow our step by step solution on how to calculate Time Period for Vibrations?

FIRST Step Consider the formula

t p = 2 \cdot π \cdot \sqrt{\frac{I d}{q}}

Next Step Substitute values of Variables

∴

t p = 2 \cdot π \cdot \sqrt{\frac{6.2kg·m²}{5.4N/m}}

Next Step Substitute values of Constants

∴

t p = 2 \cdot 3.1416 \cdot \sqrt{\frac{6.2kg·m²}{5.4N/m}}

Next Step Prepare to Evaluate

∴

t p = 2 \cdot 3.1416 \cdot \sqrt{\frac{6.2}{5.4}}

Next Step Evaluate

∴

t p = 6.73253830767135s

LAST Step Rounding Answer

∴

t p = 6.7325s

Time Period for Vibrations Formula Elements

Variables

Constants

Functions

Time Period

Time Period is the time taken by the shaft to complete one oscillation or vibration about its axis in a torsional vibration system.

Symbol: t_p

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period

Mass Moment of Inertia of Disc

Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.

Symbol: I_d

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Mass Moment of Inertia of Disc

Torsional Stiffness

torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.

Symbol: q

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Torsional Stiffness

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 in Natural Frequency of Free Torsional Vibrations category

Go Moment of Inertia of Disc using Natural Frequency of Vibration

I d = \frac{q}{{(2 \cdot π \cdot f n)}^{2}}

Go Torsional Stiffness of Shaft given Natural Frequency of Vibration

q = {(2 \cdot π \cdot f n)}^{2} \cdot I d

Go Moment of Inertia of Disc given Time Period of Vibration

I d = \frac{{t p}^{2} \cdot q}{{(2 \cdot π)}^{2}}

Go Torsional Stiffness of Shaft given Time Period of Vibration

q = \frac{{(2 \cdot π)}^{2} \cdot I d}{{(t p)}^{2}}

How to Evaluate Time Period for Vibrations?

Time Period for Vibrations evaluator uses Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness) to evaluate the Time Period, Time Period for Vibrations formula is defined as the time taken by an object to complete one oscillation or cycle in a torsional vibration system, which is a type of vibration that occurs when an object is twisted or rotated around a fixed axis, and is an important concept in mechanical engineering and physics. Time Period is denoted by t_p symbol.

How to evaluate Time Period for Vibrations using this online evaluator? To use this online evaluator for Time Period for Vibrations, enter Mass Moment of Inertia of Disc (I_d) & Torsional Stiffness (q) and hit the calculate button.

FAQs on Time Period for Vibrations

What is the formula to find Time Period for Vibrations?

The formula of Time Period for Vibrations is expressed as Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness). Here is an example- 6.732538 = 2*pi*sqrt(6.2/5.4).

How to calculate Time Period for Vibrations?

With Mass Moment of Inertia of Disc (I_d) & Torsional Stiffness (q) we can find Time Period for Vibrations using the formula - Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Time Period for Vibrations be negative?

No, the Time Period for Vibrations, measured in Time cannot be negative.

Which unit is used to measure Time Period for Vibrations?

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

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Time Period for Vibrations Formula

Time Period for Vibrations Example

Time Period for Vibrations Solution

Time Period for Vibrations Formula Elements

Other formulas in Natural Frequency of Free Torsional Vibrations category

How to Evaluate Time Period for Vibrations?

FAQs on Time Period for Vibrations

Variable Name