Peak Time Calculator

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Second Order System

Fundamental Parameters

✖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 to oscillate at a particular frequency.ⓘ Damped Natural Frequency [ω_d]

+10%

-10%

✖Peak time is 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 [t_p]

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Formula

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Peak Time

Formula

`"t"_{"p"} = pi/"ω"_{"d"}`

Example

`"0.137307s"=pi/"22.88Hz"`

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Peak Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

Peak Time = pi/Damped Natural Frequency
t_p = pi/ω_d
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Peak Time - (Measured in Second) - Peak time is simply the time required by response to reach its first peak i.e. the peak of first cycle of oscillation, or first overshoot.
Damped Natural Frequency - (Measured in Hertz) - 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 to oscillate at a particular frequency.

STEP 1: Convert Input(s) to Base Unit

Damped Natural Frequency: 22.88 Hertz --> 22.88 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_p = pi/ω_d --> pi/22.88

Evaluating ... ...

t_p = 0.13730737122333

STEP 3: Convert Result to Output's Unit

0.13730737122333 Second --> No Conversion Required

FINAL ANSWER

0.13730737122333 ≈ 0.137307 Second <-- Peak Time

(Calculation completed in 00.020 seconds)

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Credits

Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Calculator and 500+ more calculators!

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< 17 Second Order System Calculators

Time Response in Overdamped Case

Go Time Response for Second Order System = 1-(e^(-(Overdamping Ratio-(sqrt((Overdamping Ratio^2)-1)))*(Natural Frequency of Oscillation*Time Period for Oscillations))/(2*sqrt((Overdamping Ratio^2)-1)*(Overdamping Ratio-sqrt((Overdamping Ratio^2)-1))))

Time Response of Critically Damped System

Go Time Response for Second Order System = 1-e^(-Natural Frequency of Oscillation*Time Period for Oscillations)-(e^(-Natural Frequency of Oscillation*Time Period for Oscillations)*Natural Frequency of Oscillation*Time Period for Oscillations)

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

Rise Time given Damping Ratio

Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Time Response in Undamped Case

Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)

Peak Time given Damping Ratio

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

First Peak Undershoot

Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Time of Peak Overshoot in Second Order System

Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency

Rise Time given Damped Natural Frequency

Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Delay Time

Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

Setting Time when Tolerance is 2 Percent

Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

Setting Time when Tolerance is 5 Percent

Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

< 16 Second Order System Calculators

Time Response in Overdamped Case

Time Response of Critically Damped System

Rise Time given Damping Ratio

Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Time Response in Undamped Case

Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)

Peak Time given Damping Ratio

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

First Peak Undershoot

Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Time of Peak Overshoot in Second Order System

Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency

Rise Time given Damped Natural Frequency

Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Delay Time

Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

Setting Time when Tolerance is 2 Percent

Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

Setting Time when Tolerance is 5 Percent

Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

< 25 Control System Design Calculators

Time Response in Overdamped Case

Time Response of Critically Damped System

Bandwidth Frequency given Damping Ratio

Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

Rise Time given Damping Ratio

Go Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))

Percentage Overshoot

Go Percentage Overshoot = 100*(e^((-Damping Ratio*pi)/(sqrt(1-(Damping Ratio^2)))))

Time Response in Undamped Case

Go Time Response for Second Order System = 1-cos(Natural Frequency of Oscillation*Time Period for Oscillations)

Peak Time given Damping Ratio

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

First Peak Undershoot

Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Gain-Bandwidth Product

Go Gain-Bandwidth Product = modulus(Amplifier Gain in Mid Band)*Amplifier Bandwidth

Resonant Frequency

Go Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2)

Number of Oscillations

Go Number of Oscillations = (Setting Time*Damped Natural Frequency)/(2*pi)

Time of Peak Overshoot in Second Order System

Go Time of Peak Overshoot = ((2*Kth Value-1)*pi)/Damped Natural Frequency

Rise Time given Damped Natural Frequency

Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Steady State Error for Type Zero System

Go Steady State Error = Coefficient Value/(1+Position of Error Constant)

Delay Time

Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Steady State Error for Type 2 System

Go Steady State Error = Coefficient Value/Acceleration Error Constant

Time Period of Oscillations

Go Time Period for Oscillations = (2*pi)/Damped Natural Frequency

Steady State Error for Type 1 System

Go Steady State Error = Coefficient Value/Velocity Error Constant

Setting Time when Tolerance is 2 Percent

Go Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

Setting Time when Tolerance is 5 Percent

Go Setting Time = 3/(Damping Ratio*Damped Natural Frequency)

Number of Asymptotes

Go Number of Asymptotes = Number of Poles-Number of Zeroes

Peak Time

Go Peak Time = pi/Damped Natural Frequency

Q-Factor

Go Q Factor = 1/(2*Damping Ratio)

Rise Time given Delay Time

Go Rise Time = 1.5*Delay Time

Peak Time Formula

Peak Time = pi/Damped Natural Frequency
t_p = pi/ω_d

What is the peak data rate?

Peak data rate is the fastest data transfer rate for a device, typically available in short bursts during transfer activity, and not sustainable for long periods of time.

How to Calculate Peak Time?

Peak Time calculator uses Peak Time = pi/Damped Natural Frequency to calculate 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 calculate Peak Time using this online calculator? To use this online calculator for Peak Time, enter Damped Natural Frequency (ω_d) and hit the calculate button. Here is how the Peak Time calculation can be explained with given input values -> 0.137307 = pi/22.88.

FAQ

What is 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 and is represented as t_p = pi/ω_d or Peak Time = pi/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 to oscillate at a particular frequency.

How to calculate 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 is calculated using Peak Time = pi/Damped Natural Frequency. To calculate Peak Time, you need Damped Natural Frequency (ω_d). With our tool, you need to enter the respective value for Damped Natural Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Peak Time?

In this formula, Peak Time uses Damped Natural Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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