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Time Period of Oscillations using Time Constant and Damping Factor Formula

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

T = \frac{2 \cdot π \cdot 𝜏}{\sqrt{1 - ({(ζ)}^{2})}}

T - Time Period of Oscillations?𝜏 - Time Constant?ζ - Damping Factor?π - Archimedes' constant?

Time Period of Oscillations using Time Constant and Damping Factor Example

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Here is how the Time Period of Oscillations using Time Constant and Damping Factor equation looks like with Values.

Here is how the Time Period of Oscillations using Time Constant and Damping Factor equation looks like with Units.

Here is how the Time Period of Oscillations using Time Constant and Damping Factor equation looks like.

21.7656 = \frac{2 \cdot 3.1416 \cdot 3}{\sqrt{1 - ({(0.5)}^{2})}}

21.7656s = \frac{2 \cdot 3.1416 \cdot 3s}{\sqrt{1 - ({(0.5)}^{2})}}

21.7656 = \frac{2 \cdot 3.1416 \cdot 3}{\sqrt{1 - ({(0.5)}^{2})}}

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Time Period of Oscillations using Time Constant and Damping Factor Solution

Follow our step by step solution on how to calculate Time Period of Oscillations using Time Constant and Damping Factor?

FIRST Step Consider the formula

T = \frac{2 \cdot π \cdot 𝜏}{\sqrt{1 - ({(ζ)}^{2})}}

Next Step Substitute values of Variables

∴

T = \frac{2 \cdot π \cdot 3s}{\sqrt{1 - ({(0.5)}^{2})}}

Next Step Substitute values of Constants

∴

T = \frac{2 \cdot 3.1416 \cdot 3s}{\sqrt{1 - ({(0.5)}^{2})}}

Next Step Prepare to Evaluate

∴

T = \frac{2 \cdot 3.1416 \cdot 3}{\sqrt{1 - ({(0.5)}^{2})}}

Next Step Evaluate

∴

T = 21.7655923708106s

LAST Step Rounding Answer

∴

T = 21.7656s

Time Period of Oscillations using Time Constant and Damping Factor Formula Elements

Variables

Constants

Functions

Time Period of Oscillations

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

Symbol: T

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period of Oscillations

Time Constant

Time Constant (𝜏) is the time required by the response to reach 63.2% of its ultimate value. If 𝜏 is high that means system will response fast.

Symbol: 𝜏

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Constant

Damping Factor

Damping Factor is a measure describing how rapidly the oscillations decay from one bounce to the next.

Symbol: ζ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Damping Factor

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)

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How to Evaluate Time Period of Oscillations using Time Constant and Damping Factor?

Time Period of Oscillations using Time Constant and Damping Factor evaluator uses Time Period of Oscillations = (2*pi*Time Constant)/(sqrt(1-((Damping Factor)^2))) to evaluate the Time Period of Oscillations, Time Period of Oscillations using Time Constant and Damping Factor formula is defined as the smallest interval of time in which a system undergoing oscillation returns to the state it was in at a time arbitrarily chosen as the beginning of the oscillation. Time Period of Oscillations is denoted by T symbol.

How to evaluate Time Period of Oscillations using Time Constant and Damping Factor using this online evaluator? To use this online evaluator for Time Period of Oscillations using Time Constant and Damping Factor, enter Time Constant (𝜏) & Damping Factor (ζ) and hit the calculate button.

FAQs on Time Period of Oscillations using Time Constant and Damping Factor

What is the formula to find Time Period of Oscillations using Time Constant and Damping Factor?

The formula of Time Period of Oscillations using Time Constant and Damping Factor is expressed as Time Period of Oscillations = (2*pi*Time Constant)/(sqrt(1-((Damping Factor)^2))). Here is an example- 21.76559 = (2*pi*3)/(sqrt(1-((0.5)^2))).

How to calculate Time Period of Oscillations using Time Constant and Damping Factor?

With Time Constant (𝜏) & Damping Factor (ζ) we can find Time Period of Oscillations using Time Constant and Damping Factor using the formula - Time Period of Oscillations = (2*pi*Time Constant)/(sqrt(1-((Damping Factor)^2))). This formula also uses Archimedes' constant and Square Root Function function(s).

Can the Time Period of Oscillations using Time Constant and Damping Factor be negative?

No, the Time Period of Oscillations using Time Constant and Damping Factor, measured in Time cannot be negative.

Which unit is used to measure Time Period of Oscillations using Time Constant and Damping Factor?

Time Period of Oscillations using Time Constant and Damping Factor is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time Period of Oscillations using Time Constant and Damping Factor can be measured.

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Time Period of Oscillations using Time Constant and Damping Factor Formula

Time Period of Oscillations using Time Constant and Damping Factor Example

Time Period of Oscillations using Time Constant and Damping Factor Solution

Time Period of Oscillations using Time Constant and Damping Factor Formula Elements

Other formulas in Process Dynamics and Control category

How to Evaluate Time Period of Oscillations using Time Constant and Damping Factor?

FAQs on Time Period of Oscillations using Time Constant and Damping Factor

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