Amplitude Reduction Factor Calculator

✖The Frequency Constant for Calculation is the constant whose value is equal to the damping coefficient divided by twice of suspended mass.ⓘ Frequency Constant for Calculation [a]			+10% -10%
✖Time Period is the time taken by a complete cycle of the wave to pass a point.ⓘ Time Period [t_p]			+10% -10%

✖The amplitude reduction factor is the ratio of any two successive amplitudes on the same side of the mean position.ⓘ Amplitude Reduction Factor [A_r]

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Amplitude Reduction Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Amplitude Reduction Factor = e^(Frequency Constant for Calculation*Time Period)
A_r = e^(a*t_p)
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: 0.9 Second --> 0.9 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_r = e^(a*t_p) --> e^(0.2*0.9)

Evaluating ... ...

A_r = 1.19721736312181

STEP 3: Convert Result to Output's Unit

1.19721736312181 --> No Conversion Required

FINAL ANSWER

1.19721736312181 ≈ 1.197217 <-- Amplitude Reduction Factor

(Calculation completed in 00.006 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Frequency of Free Damped Vibrations » Amplitude Reduction Factor

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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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< Frequency of Free Damped Vibrations Calculators

Condition for Critical Damping

LaTeX Go Critical Damping Coefficient = 2*Mass Suspended from Spring*sqrt(Stiffness of Spring/Mass Suspended from Spring)

Damping Factor given Natural Frequency

LaTeX Go Damping Ratio = Damping Coefficient/(2*Mass Suspended from Spring*Natural Circular Frequency)

Critical Damping Coefficient

LaTeX Go Critical Damping Coefficient = 2*Mass Suspended from Spring*Natural Circular Frequency

Damping Factor

LaTeX Go Damping Ratio = Damping Coefficient/Critical Damping Coefficient

Amplitude Reduction Factor Formula

LaTeX Go

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

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, Amplitude Reduction Factor formula is defined as a measure of the reduction in amplitude of a vibrating system due to damping, providing a quantitative representation of the energy loss in a free damped vibration, which is essential in understanding the behavior of oscillating systems in various fields such as physics and engineering. Amplitude Reduction Factor is denoted by A_r 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 (t_p) and hit the calculate button. Here is how the Amplitude Reduction Factor calculation can be explained with given input values -> 1.822119 = e^(0.2*0.9).

FAQ

What is Amplitude Reduction Factor?

Amplitude Reduction Factor formula is defined as a measure of the reduction in amplitude of a vibrating system due to damping, providing a quantitative representation of the energy loss in a free damped vibration, which is essential in understanding the behavior of oscillating systems in various fields such as physics and engineering and is represented as A_r = e^(a*t_p) 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?

Amplitude Reduction Factor formula is defined as a measure of the reduction in amplitude of a vibrating system due to damping, providing a quantitative representation of the energy loss in a free damped vibration, which is essential in understanding the behavior of oscillating systems in various fields such as physics and engineering 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 (t_p). 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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