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Peak Time given Damping Ratio Formula

GoPeak Time Formula

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Peak Time is simply the time required by the response to reach its first peak i.e. the peak of the first cycle of oscillation, or first overshoot. Check FAQs

t p = \frac{π}{ω n \cdot \sqrt{1 - ζ^{2}}}

t_p - Peak Time?ω_n - Natural Frequency of Oscillation?ζ - Damping Ratio?π - Archimedes' constant?

Peak Time given Damping Ratio Example

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Here is how the Peak Time given Damping Ratio equation looks like with Values.

Here is how the Peak Time given Damping Ratio equation looks like with Units.

Here is how the Peak Time given Damping Ratio equation looks like.

0.1373 = \frac{3.1416}{23 \cdot \sqrt{1 - {0.1}^{2}}}

0.1373s = \frac{3.1416}{23Hz \cdot \sqrt{1 - {0.1}^{2}}}

0.1373 = \frac{3.1416}{23 \cdot \sqrt{1 - {0.1}^{2}}}

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Peak Time given Damping Ratio Solution

Follow our step by step solution on how to calculate Peak Time given Damping Ratio?

FIRST Step Consider the formula

t p = \frac{π}{ω n \cdot \sqrt{1 - ζ^{2}}}

Next Step Substitute values of Variables

∴

t p = \frac{π}{23Hz \cdot \sqrt{1 - {0.1}^{2}}}

Next Step Substitute values of Constants

∴

t p = \frac{3.1416}{23Hz \cdot \sqrt{1 - {0.1}^{2}}}

Next Step Prepare to Evaluate

∴

t p = \frac{3.1416}{23 \cdot \sqrt{1 - {0.1}^{2}}}

Next Step Evaluate

∴

t p = 0.137279105086882s

LAST Step Rounding Answer

∴

t p = 0.1373s

Peak Time given Damping Ratio Formula Elements

Variables

Constants

Functions

Peak Time

Peak Time is simply the time required by the response to reach its first peak i.e. the peak of the first cycle of oscillation, or first overshoot.

Symbol: t_p

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Peak Time

Natural Frequency of Oscillation

The Natural Frequency of Oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position.

Symbol: ω_n

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Natural Frequency of Oscillation

Damping Ratio

Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

Symbol: ζ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Damping Ratio

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 Peak Time

Go Peak Time

t p = \frac{π}{ω d}

Other formulas in Second Order System category

Go Bandwidth Frequency given Damping Ratio

f b = ω n \cdot (\sqrt{1 - (2 \cdot ζ^{2})} + \sqrt{ζ^{4} - (4 \cdot ζ^{2}) + 2})

Go Delay Time

t d = \frac{1 + (0.7 \cdot ζ)}{ω n}

Go First Peak Overshoot

M o = e^{- \frac{π \cdot ζ}{\sqrt{1 - ζ^{2}}}}

Go First Peak Undershoot

M u = e^{- \frac{2 \cdot ζ \cdot π}{\sqrt{1 - ζ^{2}}}}

How to Evaluate Peak Time given Damping Ratio?

Peak Time given Damping Ratio evaluator uses Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)) to evaluate the Peak Time, The Peak Time given damping ratio formula is defined as the time required by the response to reach its first peak i.e. the peak of the first cycle of oscillation, or the first overshoot the response curve reaches to its maximum value. Peak Time is denoted by t_p symbol.

How to evaluate Peak Time given Damping Ratio using this online evaluator? To use this online evaluator for Peak Time given Damping Ratio, enter Natural Frequency of Oscillation (ω_n) & Damping Ratio (ζ) and hit the calculate button.

FAQs on Peak Time given Damping Ratio

What is the formula to find Peak Time given Damping Ratio?

The formula of Peak Time given Damping Ratio is expressed as Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)). Here is an example- 0.137279 = pi/(23*sqrt(1-0.1^2)).

How to calculate Peak Time given Damping Ratio?

With Natural Frequency of Oscillation (ω_n) & Damping Ratio (ζ) we can find Peak Time given Damping Ratio using the formula - Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Peak Time?

Here are the different ways to Calculate Peak Time-

Peak Time=pi/Damped Natural Frequency

Can the Peak Time given Damping Ratio be negative?

No, the Peak Time given Damping Ratio, measured in Time cannot be negative.

Which unit is used to measure Peak Time given Damping Ratio?

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

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Peak Time given Damping Ratio Formula

​GoPeak Time Formula

Peak Time given Damping Ratio Example

Peak Time given Damping Ratio Solution

Peak Time given Damping Ratio Formula Elements

Other Formulas to find Peak Time

Other formulas in Second Order System category

How to Evaluate Peak Time given Damping Ratio?

FAQs on Peak Time given Damping Ratio

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GoPeak Time Formula