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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 oscillating at a particular frequency.ⓘ Damped Natural Frequency [ω_d]

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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.ⓘ Peak Time [t_p]

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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 the response to reach its first peak i.e. the peak of the 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 oscillating 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 00.004 seconds)

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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< Second Order System Calculators

Bandwidth Frequency given Damping Ratio

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

First Peak Undershoot

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

First Peak Overshoot

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

Delay Time

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

< Second Order System Calculators

First Peak Overshoot

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

Rise Time given Damped Natural Frequency

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

Delay Time

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

Peak Time

LaTeX Go Peak Time = pi/Damped Natural Frequency

< Control System Design Calculators

Bandwidth Frequency given Damping Ratio

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

First Peak Undershoot

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

First Peak Overshoot

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

Delay Time

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

Peak Time Formula

LaTeX Go

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 oscillating 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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