Amplitude Reduction Factor Solution

STEP 0: Pre-Calculation Summary
Formula Used
Amplitude Reduction Factor = e^(Frequency Constant for Calculation*Time Period)
Areduction = e^(a*tp)
This formula uses 1 Constants, 3 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Variables Used
Amplitude Reduction Factor - The amplitude reduction factor is the ratio of any two successive amplitudes on the same side of the mean position.
Frequency Constant for Calculation - (Measured in Hertz) - The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.
Time Period - (Measured in Second) - Time Period is the time taken by a complete cycle of the wave to pass a point.
STEP 1: Convert Input(s) to Base Unit
Frequency Constant for Calculation: 0.2 Hertz --> 0.2 Hertz No Conversion Required
Time Period: 3 Second --> 3 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Areduction = e^(a*tp) --> e^(0.2*3)
Evaluating ... ...
Areduction = 1.82211880039051
STEP 3: Convert Result to Output's Unit
1.82211880039051 --> No Conversion Required
FINAL ANSWER
1.82211880039051 1.822119 <-- Amplitude Reduction Factor
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Indian Institute of Information Technology (IIIT), Guwahati
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9 Frequency of Free Damped Vibrations Calculators

Logarithmic Decrement using Natural Frequency
Go Logarithmic Decrement = (Frequency Constant for Calculation*2*pi)/(sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2))
Logarithmic Decrement using Circular Damping Coefficient
Go Logarithmic Decrement = (2*pi*Damping Coefficient)/(sqrt(Critical Damping Coefficient^2-Damping Coefficient^2))
Condition for Critical Damping
Go Critical Damping Coefficient = 2*Mass Suspended from Spring*sqrt(Stiffness of Spring/Mass Suspended from Spring)
Logarithmic Decrement using Circular Damped Frequency
Go Logarithmic Decrement = Frequency Constant for Calculation*(2*pi)/Circular Damped Frequency
Damping Factor given Natural Frequency
Go Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency)
Critical Damping Coefficient
Go Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency
Amplitude Reduction Factor
Go Amplitude Reduction Factor = e^(Frequency Constant for Calculation*Time Period)
Logarithmic Decrement
Go Logarithmic Decrement = Frequency Constant for Calculation*Time Period
Damping Factor
Go Damping Ratio = Damping Coefficient/Critical Damping Coefficient

Amplitude Reduction Factor Formula

Amplitude Reduction Factor = e^(Frequency Constant for Calculation*Time Period)
Areduction = e^(a*tp)

What is damped free vibration?

Damped vibration occurs when the energy of a vibrating system is gradually dissipated by friction and other resistances, the vibrations are said to be damped. The vibrations gradually reduce or change in frequency or intensity or cease and the system rests in its equilibrium position.

How to Calculate Amplitude Reduction Factor?

Amplitude Reduction Factor calculator uses Amplitude Reduction Factor = e^(Frequency Constant for Calculation*Time Period) to calculate the Amplitude Reduction Factor, The Amplitude reduction factor formula is defined as the ratio of successive values of the amplitude on the same side of the mean position. Amplitude Reduction Factor is denoted by Areduction symbol.

How to calculate Amplitude Reduction Factor using this online calculator? To use this online calculator for Amplitude Reduction Factor, enter Frequency Constant for Calculation (a) & Time Period (tp) and hit the calculate button. Here is how the Amplitude Reduction Factor calculation can be explained with given input values -> 1.061837 = e^(0.2*3).

FAQ

What is Amplitude Reduction Factor?
The Amplitude reduction factor formula is defined as the ratio of successive values of the amplitude on the same side of the mean position and is represented as Areduction = e^(a*tp) or Amplitude Reduction Factor = e^(Frequency Constant for Calculation*Time Period). The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass & Time Period is the time taken by a complete cycle of the wave to pass a point.
How to calculate Amplitude Reduction Factor?
The Amplitude reduction factor formula is defined as the ratio of successive values of the amplitude on the same side of the mean position is calculated using Amplitude Reduction Factor = e^(Frequency Constant for Calculation*Time Period). To calculate Amplitude Reduction Factor, you need Frequency Constant for Calculation (a) & Time Period (tp). With our tool, you need to enter the respective value for Frequency Constant for Calculation & Time Period 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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