For a damped single degree of freedom system with damping ratio of 0.1, ratio of two successive peak amplitudes of free vibration is ___________ (accurate to two decimal places)Correct answer is '1.75 to 1.95'. Can you explain this answer?

Question

Answer

Damped Single Degree of Freedom System

A damped single degree of freedom system refers to a system that has one degree of freedom and has a damping coefficient. The system undergoes free vibration when it is displaced from its equilibrium position and released.

Damping Ratio

The damping ratio is the ratio of the actual damping coefficient of a system to its critical damping coefficient. It is represented by the symbol ζ (zeta) and is a dimensionless quantity. The damping ratio determines the type of response of the system, whether it is underdamped, critically damped, or overdamped.

Two Successive Peak Amplitudes of Free Vibration

The ratio of two successive peak amplitudes of free vibration is the ratio of the amplitude of the second peak to the amplitude of the first peak. In other words, it is the ratio of the maximum displacement of the system during the second oscillation to the maximum displacement during the first oscillation.

Calculation of Ratio of Two Successive Peak Amplitudes of Free Vibration

The ratio of two successive peak amplitudes of free vibration for a damped single degree of freedom system with damping ratio ζ can be calculated using the following formula:

Ratio = exp(πζ/√(1-ζ²))

For a damping ratio of 0.1, the ratio of two successive peak amplitudes of free vibration is:

Ratio = exp(π*0.1/√(1-0.1²)) = 1.75 to 1.95 (accurate to two decimal places)

Therefore, the ratio of two successive peak amplitudes of free vibration for a damped single degree of freedom system with a damping ratio of 0.1 is between 1.75 and 1.95.

Similar GATE Doubts

The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1kg, stiffness 100 N/m and viscous damping coefficient of 25 N.s/m is _______ Correct answer is between '1.24,1.26'. Can you explain this answer?

In under damped vibrating system, if x1 and x2 are the successive values of the amplitude on the same side of the mean position, then the logarithmic decrement is equal to

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