Effect of Damping Study Notes for GATE ME Exam

Damped Systems

• Damping is an effect that causes a reduction in the amplitude of an oscillation as a result of energy being drained from the system to overcame frictional/other Resistive forces.
• These are the systems in which kinetic friction is zero. Technical Name of Kinetic friction in any Vibrations system is known as, Damping.

Damping in Any System:

                                                   

Types of damping systems

Overdamped System(ζ>1): No vibrations will be present in an over-damped system:

Critically Damped Systems(ζ=1):

Note: Critical damping response is much faster than overdamping response i.e. in critically-damped systems, the body once displaced comes into its Equilibrium Position much faster than that in overdamped systems.

Under Damped Systems (ζ < 1):

 

 

 

 

Hence, the Amplitude of under-Damped Vibrations is not constant and it decreases exponentially w.r.t. time.

Logarithmic Decrement (δ ):

 

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