Time Period of Oscillations using Time Constant and Damping Factor Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time period of oscillations = (2*pi*Time Constant)/ (sqrt(1-((Damping Factor)^2)))
T = (2*pi*𝜏)/ (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 - Squre root function, sqrt(Number)
Variables Used
Time period of oscillations - (Measured in Second) - The time period of oscillations is the time taken by a complete cycle of the wave to pass a point.
Time Constant - (Measured in Second) - Time Constant (𝜏) is the time required by the response to reach 63.2% of its ultimate value. If 𝜏 is high that means system will response fast.
Damping Factor - Damping Factor is a measure describing how rapidly the oscillations decay from one bounce to the next.
STEP 1: Convert Input(s) to Base Unit
Time Constant: 5 Second --> 5 Second No Conversion Required
Damping Factor: 0.5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = (2*pi*𝜏)/ (sqrt(1-((ζ)^2))) --> (2*pi*5)/ (sqrt(1-((0.5)^2)))
Evaluating ... ...
T = 36.2759872846844
STEP 3: Convert Result to Output's Unit
36.2759872846844 Second --> No Conversion Required
FINAL ANSWER
36.2759872846844 Second <-- Time period of oscillations
(Calculation completed in 00.000 seconds)

Credits

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University School of Chemical Technology-USCT (GGSIPU), New Delhi
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Time Period of Oscillations using Time Constant and Damping Factor Formula

Time period of oscillations = (2*pi*Time Constant)/ (sqrt(1-((Damping Factor)^2)))
T = (2*pi*𝜏)/ (sqrt(1-((ζ)^2)))

What is Time Constant?

Time constant means how fast the system reaches the final value. As smaller the time constant, as faster is the system response. If time constant is larger, system goes to move slow. The time constant can be defined as the time it takes for the step response to rise up to 63% or 0.63 of its final value. The reciprocal of time constant, is 1/seconds or frequency.

What is Damping factor?

The damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance.

How to Calculate Time Period of Oscillations using Time Constant and Damping Factor?

Time Period of Oscillations using Time Constant and Damping Factor calculator uses Time period of oscillations = (2*pi*Time Constant)/ (sqrt(1-((Damping Factor)^2))) to calculate the Time period of oscillations, Time Period of Oscillations using Time Constant and Damping Factor formula is defined as the smallest interval of time in which a system undergoing oscillation returns to the state it was in at a time arbitrarily chosen as the beginning of the oscillation. Time period of oscillations is denoted by T symbol.

How to calculate Time Period of Oscillations using Time Constant and Damping Factor using this online calculator? To use this online calculator for Time Period of Oscillations using Time Constant and Damping Factor, enter Time Constant (𝜏) & Damping Factor (ζ) and hit the calculate button. Here is how the Time Period of Oscillations using Time Constant and Damping Factor calculation can be explained with given input values -> 36.27599 = (2*pi*5)/ (sqrt(1-((0.5)^2))).

FAQ

What is Time Period of Oscillations using Time Constant and Damping Factor?
Time Period of Oscillations using Time Constant and Damping Factor formula is defined as the smallest interval of time in which a system undergoing oscillation returns to the state it was in at a time arbitrarily chosen as the beginning of the oscillation and is represented as T = (2*pi*𝜏)/ (sqrt(1-((ζ)^2))) or Time period of oscillations = (2*pi*Time Constant)/ (sqrt(1-((Damping Factor)^2))). Time Constant (𝜏) is the time required by the response to reach 63.2% of its ultimate value. If 𝜏 is high that means system will response fast & Damping Factor is a measure describing how rapidly the oscillations decay from one bounce to the next.
How to calculate Time Period of Oscillations using Time Constant and Damping Factor?
Time Period of Oscillations using Time Constant and Damping Factor formula is defined as the smallest interval of time in which a system undergoing oscillation returns to the state it was in at a time arbitrarily chosen as the beginning of the oscillation is calculated using Time period of oscillations = (2*pi*Time Constant)/ (sqrt(1-((Damping Factor)^2))). To calculate Time Period of Oscillations using Time Constant and Damping Factor, you need Time Constant (𝜏) & Damping Factor (ζ). With our tool, you need to enter the respective value for Time Constant & Damping Factor 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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