HCF of three numbers

Delay Time Calculator

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Second Order System Fundamental Parameters

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

✖Delay Time is the time required to reach at 50% of its final value by a time response signal during its first cycle of oscillation.ⓘ Delay Time [t_d]

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Formula

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Delay Time

Formula

t d = \frac{1 + (0.7 \cdot ζ)}{ω n}

Example

0.046522 s = \frac{1 + (0.7 \cdot 0.1)}{23 Hz}

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Delay Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation
t_d = (1+(0.7*ζ))/ω_n
This formula uses 3 Variables

Variables Used

Delay Time - (Measured in Second) - Delay Time is the time required to reach at 50% of its final value by a time response signal during its first cycle of oscillation.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_d = (1+(0.7*ζ))/ω_n --> (1+(0.7*0.1))/23

Evaluating ... ...

t_d = 0.0465217391304348

STEP 3: Convert Result to Output's Unit

0.0465217391304348 Second --> No Conversion Required

FINAL ANSWER

0.0465217391304348 ≈ 0.046522 Second <-- Delay 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

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

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)))

Delay Time

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

< Second Order System Calculators

First Peak Overshoot

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

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

Peak Time

Go Peak Time = pi/Damped Natural Frequency

< Control System Design Calculators

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))

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)))

Delay Time

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

Delay Time Formula

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

How do you measure delay time?

The delay time is obtained by measuring a phase difference ϑ between the signals at the input and output transducers of the delay line with frequencies under test. The delay time is more precisely obtained by measuring the ϑ at a constant frequency within the bandwidth of the delay line.

How to Calculate Delay Time?

Delay Time calculator uses Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation to calculate the Delay Time, Delay Time is defined as the solution to the first-order differential equation with time delay is obtained by replacing all variables t with t−θp t - θ p and applying the conditional result based on the time in relation to the time delay, θp . Delay Time is denoted by t_d symbol.

How to calculate Delay Time using this online calculator? To use this online calculator for Delay Time, enter Damping Ratio (ζ) & Natural Frequency of Oscillation (ω_n) and hit the calculate button. Here is how the Delay Time calculation can be explained with given input values -> 0.046522 = (1+(0.7*0.1))/23.

FAQ

What is Delay Time?

Delay Time is defined as the solution to the first-order differential equation with time delay is obtained by replacing all variables t with t−θp t - θ p and applying the conditional result based on the time in relation to the time delay, θp and is represented as t_d = (1+(0.7*ζ))/ω_n or Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation. Damping Ratio in control system is defined as the ratio with which any signal gets decayed & 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.

How to calculate Delay Time?

Delay Time is defined as the solution to the first-order differential equation with time delay is obtained by replacing all variables t with t−θp t - θ p and applying the conditional result based on the time in relation to the time delay, θp is calculated using Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation. To calculate Delay Time, you need Damping Ratio (ζ) & Natural Frequency of Oscillation (ω_n). With our tool, you need to enter the respective value for Damping Ratio & Natural Frequency of Oscillation and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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