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Rise Time given Damping Ratio Calculator

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✖Phase Shift is defined as the shift or difference between the angles or phases of two unique signals.ⓘ Phase Shift [Φ]
+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 [ωn]
+10%
-10%
✖Damping Ratio in control system is defined as the ratio with which any signal gets decayed.ⓘ Damping Ratio [ζ]
+10%
-10%
✖Rise Time is the time required to reach at final value by a under damped time response signal during its first cycle of oscillation.ⓘ Rise Time given Damping Ratio [tr]
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Rise Time given Damping Ratio

Formula
`"t"_{"r"} = (pi-("Φ"*pi/180))/("ω"_{"n"}*sqrt(1-"ζ"^2))`

Example
`"0.137073s"=(pi-("0.27rad"*pi/180))/("23Hz"*sqrt(1-("0.1")^2))`

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Rise Time given Damping Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
tr = (pi-(Φ*pi/180))/(ωn*sqrt(1-ζ^2))
This formula uses 1 Constants, 1 Functions, 4 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
Rise Time - (Measured in Second) - Rise Time is the time required to reach at final value by a under damped time response signal during its first cycle of oscillation.
Phase Shift - (Measured in Radian) - Phase Shift is defined as the shift or difference between the angles or phases of two unique signals.
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
Phase Shift: 0.27 Radian --> 0.27 Radian No Conversion Required
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
tr = (pi-(Φ*pi/180))/(ωn*sqrt(1-ζ^2)) --> (pi-(0.27*pi/180))/(23*sqrt(1-0.1^2))
Evaluating ... ...
tr = 0.137073186429251
STEP 3: Convert Result to Output's Unit
0.137073186429251 Second --> No Conversion Required
FINAL ANSWER
0.137073186429251 ≈ 0.137073 Second <-- Rise Time
(Calculation completed in 00.004 seconds)
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Indian Institute of Technology,Roorlee (IITR), Roorkee
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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
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)
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
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))
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

Rise Time given Damping Ratio Formula

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

What is rise time?

Rise time is the time taken for a signal to cross a specified lower voltage threshold followed by a specified upper voltage threshold. This is an important parameter in both digital and analog systems. In digital systems it describes how long a signal spends in the intermediate state between two valid logic levels. In analog systems it specifies the time taken for the output to rise from one specified level to another when the input is driven by an ideal edge with zero rise time. This indicates how well the system preserves a fast transition in the input signal.

How to Calculate Rise Time given Damping Ratio?

Rise Time given Damping Ratio calculator uses Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)) to calculate the Rise Time, The Rise time given damping ratio formula is defined as the time required for the response to rise from 0% to 100% of its final value. This is applicable for the under-damped systems. Rise Time is denoted by tr symbol.

How to calculate Rise Time given Damping Ratio using this online calculator? To use this online calculator for Rise Time given Damping Ratio, enter Phase Shift (Φ), Natural Frequency of Oscillation (ωn) & Damping Ratio (ζ) and hit the calculate button. Here is how the Rise Time given Damping Ratio calculation can be explained with given input values -> 0.137073 = (pi-(0.27*pi/180))/(23*sqrt(1-0.1^2)).

FAQ

What is Rise Time given Damping Ratio?
The Rise time given damping ratio formula is defined as the time required for the response to rise from 0% to 100% of its final value. This is applicable for the under-damped systems and is represented as tr = (pi-(Φ*pi/180))/(ωn*sqrt(1-ζ^2)) or Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)). Phase Shift is defined as the shift or difference between the angles or phases of two unique signals, 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 Rise Time given Damping Ratio?
The Rise time given damping ratio formula is defined as the time required for the response to rise from 0% to 100% of its final value. This is applicable for the under-damped systems is calculated using Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2)). To calculate Rise Time given Damping Ratio, you need Phase Shift (Φ), Natural Frequency of Oscillation (ωn) & Damping Ratio (ζ). With our tool, you need to enter the respective value for Phase Shift, 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 Rise Time?
In this formula, Rise Time uses Phase Shift, Natural Frequency of Oscillation & Damping Ratio. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Rise Time = (pi-Phase Shift)/Damped Natural Frequency
  • Rise Time = 1.5*Delay Time
  • Rise Time = (pi-Phase Shift)/Damped Natural Frequency
  • Rise Time = 1.5*Delay Time
  • Rise Time = (pi-Phase Shift)/Damped Natural Frequency
  • Rise Time = 1.5*Delay Time
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