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Peak Time given Damping Ratio Calculator

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Second Order System Fundamental Parameters

✖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.ⓘ Natural Frequency of Oscillation [ω_n]			+10% -10%
✖Damping Ratio in control system is defined as the ratio with which any signal gets decayed.ⓘ Damping Ratio [ζ]			+10% -10%

✖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 given Damping Ratio [t_p]

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Peak Time given Damping Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
t_p = pi/(ω_n*sqrt(1-ζ^2))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

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.
Natural Frequency of Oscillation - (Measured in Hertz) - 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.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

STEP 1: Convert Input(s) to Base Unit

Natural Frequency of Oscillation: 23 Hertz --> 23 Hertz No Conversion Required
Damping Ratio: 0.1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_p = pi/(ω_n*sqrt(1-ζ^2)) --> pi/(23*sqrt(1-0.1^2))

Evaluating ... ...

t_p = 0.137279105086882

STEP 3: Convert Result to Output's Unit

0.137279105086882 Second --> No Conversion Required

FINAL ANSWER

0.137279105086882 ≈ 0.137279 Second <-- Peak Time

(Calculation completed in 00.007 seconds)

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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 given Damping Ratio Formula

LaTeX Go

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

What does damping ratio depend on?

The energy dissipation is caused by material damping which basically depends on three factors: amplitude of stress, number of cycles and geometry. In the case of non-homogeneous stress distribution the geometry of the structure influences the vibration damping.

How to Calculate Peak Time given Damping Ratio?

Peak Time given Damping Ratio calculator uses Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)) to calculate 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 calculate Peak Time given Damping Ratio using this online calculator? To use this online calculator for Peak Time given Damping Ratio, enter Natural Frequency of Oscillation (ω_n) & Damping Ratio (ζ) and hit the calculate button. Here is how the Peak Time given Damping Ratio calculation can be explained with given input values -> 0.137279 = pi/(23*sqrt(1-0.1^2)).

FAQ

What is Peak Time given Damping Ratio?

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 and is represented as t_p = pi/(ω_n*sqrt(1-ζ^2)) or Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)). 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 & Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

How to calculate Peak Time given Damping Ratio?

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 is calculated using Peak Time = pi/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)). To calculate Peak Time given Damping Ratio, you need Natural Frequency of Oscillation (ω_n) & Damping Ratio (ζ). With our tool, you need to enter the respective value for Natural Frequency of Oscillation & Damping Ratio 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 Natural Frequency of Oscillation & Damping Ratio. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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