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Setting Time when Tolerance is 5 Percent Formula

GoSetting Time when Tolerance is 2 Percent Formula

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Setting Time is the time required for a response to become steady. Check FAQs

t s = \frac{3}{ζ \cdot ω d}

t_s - Setting Time?ζ - Damping Ratio?ω_d - Damped Natural Frequency?

Setting Time when Tolerance is 5 Percent Example

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With units

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Here is how the Setting Time when Tolerance is 5 Percent equation looks like with Values.

Here is how the Setting Time when Tolerance is 5 Percent equation looks like with Units.

Here is how the Setting Time when Tolerance is 5 Percent equation looks like.

1.3112 = \frac{3}{0.1 \cdot 22.88}

1.3112s = \frac{3}{0.1 \cdot 22.88Hz}

1.3112 = \frac{3}{0.1 \cdot 22.88}

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Setting Time when Tolerance is 5 Percent Solution

Follow our step by step solution on how to calculate Setting Time when Tolerance is 5 Percent?

FIRST Step Consider the formula

t s = \frac{3}{ζ \cdot ω d}

Next Step Substitute values of Variables

∴

t s = \frac{3}{0.1 \cdot 22.88Hz}

Next Step Prepare to Evaluate

∴

t s = \frac{3}{0.1 \cdot 22.88}

Next Step Evaluate

∴

t s = 1.31118881118881s

LAST Step Rounding Answer

∴

t s = 1.3112s

Setting Time when Tolerance is 5 Percent Formula Elements

Variables

Setting Time

Setting Time is the time required for a response to become steady.

Symbol: t_s

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Damping Ratio

Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

Symbol: ζ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

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.

Symbol: ω_d

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Credits

Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has created this Formula and 500+ more formulas!

Verified by Team Softusvista

Softusvista Office (Pune), India

Team Softusvista has verified this Formula and 1100+ more formulas!

Other Formulas to find Setting Time

Go Setting Time when Tolerance is 2 Percent

t s = \frac{4}{ζ \cdot ω d}

Other formulas in Second Order System category

Go Bandwidth Frequency given Damping Ratio

f b = ω n \cdot (\sqrt{1 - (2 \cdot ζ^{2})} + \sqrt{ζ^{4} - (4 \cdot ζ^{2}) + 2})

Go Delay Time

t d = \frac{1 + (0.7 \cdot ζ)}{ω n}

Go First Peak Overshoot

M o = e^{- \frac{π \cdot ζ}{\sqrt{1 - ζ^{2}}}}

Go First Peak Undershoot

M u = e^{- \frac{2 \cdot ζ \cdot π}{\sqrt{1 - ζ^{2}}}}

How to Evaluate Setting Time when Tolerance is 5 Percent?

Setting Time when Tolerance is 5 Percent evaluator uses Setting Time = 3/(Damping Ratio*Damped Natural Frequency) to evaluate the Setting Time, Setting Time when Tolerance is 5 percent is defined as the time required by the response to reach and steady with 5% of its final value. Setting Time is denoted by t_s symbol.

How to evaluate Setting Time when Tolerance is 5 Percent using this online evaluator? To use this online evaluator for Setting Time when Tolerance is 5 Percent, enter Damping Ratio (ζ) & Damped Natural Frequency (ω_d) and hit the calculate button.

FAQs on Setting Time when Tolerance is 5 Percent

What is the formula to find Setting Time when Tolerance is 5 Percent?

The formula of Setting Time when Tolerance is 5 Percent is expressed as Setting Time = 3/(Damping Ratio*Damped Natural Frequency). Here is an example- 1.311189 = 3/(0.1*22.88).

How to calculate Setting Time when Tolerance is 5 Percent?

With Damping Ratio (ζ) & Damped Natural Frequency (ω_d) we can find Setting Time when Tolerance is 5 Percent using the formula - Setting Time = 3/(Damping Ratio*Damped Natural Frequency).

What are the other ways to Calculate Setting Time?

Here are the different ways to Calculate Setting Time-

Setting Time=4/(Damping Ratio*Damped Natural Frequency)

Can the Setting Time when Tolerance is 5 Percent be negative?

No, the Setting Time when Tolerance is 5 Percent, measured in Time cannot be negative.

Which unit is used to measure Setting Time when Tolerance is 5 Percent?

Setting Time when Tolerance is 5 Percent is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Setting Time when Tolerance is 5 Percent can be measured.