Rise Time given Damped Natural Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rise Time = (pi-Phase Shift)/Damped Natural Frequency
tr = (pi-Φ)/ωd
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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.
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
Phase Shift: 0.27 Radian --> 0.27 Radian No Conversion Required
Damped Natural Frequency: 22.88 Hertz --> 22.88 Hertz No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
tr = (pi-Φ)/ωd --> (pi-0.27)/22.88
Evaluating ... ...
tr = 0.125506671922631
STEP 3: Convert Result to Output's Unit
0.125506671922631 Second --> No Conversion Required
FINAL ANSWER
0.125506671922631 0.125507 Second <-- Rise Time
(Calculation completed in 00.004 seconds)

Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
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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 Damped Natural Frequency Formula

Rise Time = (pi-Phase Shift)/Damped Natural Frequency
tr = (pi-Φ)/ωd

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 Damped Natural Frequency?

Rise Time given Damped Natural Frequency calculator uses Rise Time = (pi-Phase Shift)/Damped Natural Frequency to calculate the Rise Time, Rise time given Damped Natural Frequency formula is defined as the time required for the response to rise from 0% to 100% of its final value. This is applicable to the under-damped systems. For the over-damped systems, consider the duration from 10% to 90% of the final value. Rise Time is denoted by tr symbol.

How to calculate Rise Time given Damped Natural Frequency using this online calculator? To use this online calculator for Rise Time given Damped Natural Frequency, enter Phase Shift (Φ) & Damped Natural Frequency d) and hit the calculate button. Here is how the Rise Time given Damped Natural Frequency calculation can be explained with given input values -> 0.125507 = (pi-0.27)/22.88.

FAQ

What is Rise Time given Damped Natural Frequency?
Rise time given Damped Natural Frequency formula is defined as the time required for the response to rise from 0% to 100% of its final value. This is applicable to the under-damped systems. For the over-damped systems, consider the duration from 10% to 90% of the final value and is represented as tr = (pi-Φ)/ωd or Rise Time = (pi-Phase Shift)/Damped Natural Frequency. Phase Shift is defined as the shift or difference between the angles or phases of two unique signals & 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 Rise Time given Damped Natural Frequency?
Rise time given Damped Natural Frequency formula is defined as the time required for the response to rise from 0% to 100% of its final value. This is applicable to the under-damped systems. For the over-damped systems, consider the duration from 10% to 90% of the final value is calculated using Rise Time = (pi-Phase Shift)/Damped Natural Frequency. To calculate Rise Time given Damped Natural Frequency, you need Phase Shift (Φ) & Damped Natural Frequency d). With our tool, you need to enter the respective value for Phase Shift & 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 Rise Time?
In this formula, Rise Time uses Phase Shift & Damped Natural Frequency. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
  • Rise Time = 1.5*Delay Time
  • Rise Time = 1.5*Delay Time
  • Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
  • Rise Time = (pi-(Phase Shift*pi/180))/(Natural Frequency of Oscillation*sqrt(1-Damping Ratio^2))
  • Rise Time = 1.5*Delay Time
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