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Peak Time Formula

GoPeak Time given Damping Ratio 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 d}

t_p - Peak Time?ω_d - Damped Natural Frequency?π - Archimedes' constant?

Peak Time Example

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With units

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

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

Here is how the Peak Time equation looks like.

0.1373 = \frac{3.1416}{22.88}

0.1373s = \frac{3.1416}{22.88Hz}

0.1373 = \frac{3.1416}{22.88}

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Peak Time Solution

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

FIRST Step Consider the formula

t p = \frac{π}{ω d}

Next Step Substitute values of Variables

∴

t p = \frac{π}{22.88Hz}

Next Step Substitute values of Constants

∴

t p = \frac{3.1416}{22.88Hz}

Next Step Prepare to Evaluate

∴

t p = \frac{3.1416}{22.88}

Next Step Evaluate

∴

t p = 0.13730737122333s

LAST Step Rounding Answer

∴

t p = 0.1373s

Peak Time Formula Elements

Variables

Constants

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

Damped Natural Frequency

Damped Natural Frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue oscillating at a particular frequency.

Symbol: ω_d

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Damped Natural Frequency

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

Other Formulas to find Peak Time

Go Peak Time given Damping Ratio

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

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?

Peak Time evaluator uses Peak Time = pi/Damped Natural Frequency to evaluate the Peak Time, Peak Time formula is defined as the simply the time required by response to reach its first peak i.e. the peak of first cycle of oscillation, or first overshoot. Peak Time is denoted by t_p symbol.

How to evaluate Peak Time using this online evaluator? To use this online evaluator for Peak Time, enter Damped Natural Frequency (ω_d) and hit the calculate button.

FAQs on Peak Time

What is the formula to find Peak Time?

The formula of Peak Time is expressed as Peak Time = pi/Damped Natural Frequency. Here is an example- 0.137307 = pi/22.88.

How to calculate Peak Time?

With Damped Natural Frequency (ω_d) we can find Peak Time using the formula - Peak Time = pi/Damped Natural Frequency. This formula also uses Archimedes' constant .

What are the other ways to Calculate Peak Time?

Here are the different ways to Calculate Peak Time-

Peak Time=pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Can the Peak Time be negative?

No, the Peak Time, measured in Time cannot be negative.

Which unit is used to measure Peak Time?

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

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