Question

(1) What is the critical damping Ccr ? Try to derive the expression of mass, damping and stiffness in a single degree of freedom system

(2) What is logarithmic decline δ? The relationship with the Damping ratio?

I am not good in English, and everytime you write in cursive it takes me a lot of time to guess what the word is. So can you try not to write in cursive, I would appreciate that.

Answer 1

1) When the damping ratio (c/c_{cr or $\zeta$} ) is equal to 1 i.e damping coefficient (c) equals to critical damping coefficient (c_cr) of the single degree of freedom system or the damping coefficient equals to undamped resonant frequency of oscillator , it is called critical damping.

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2. Logarithmic decrement or logarithmic decline ($\delta$): It is the natural log of ratio of two successive amplitude of the SDOF system.

$\delta$ = (1/n) ln (x_n/x_n+1)

x_n= amplitude of n^th vibration

x_n+1= amplitude of (n+1)^th vibration

john logements Relationship with the logarithmic decrement and damping ratio 8= 208