Question

The measurements on a mechanical vibrating system show that it has a mass of 8 kg and that the springs can be combined to give an equivalent spring of stiffness 5.4 N/mm. If the vibrating system have a dashpot attached which exerts a force of 40 N when the mass has  a velocity of 1 m/s, find : 

1. critical damping coefficient, 

2.  damping factor,

3.  Logarithmic decrement, and 

4.  ratio of two consecutive amplitudes. 

Answer 1

Given : m 8 kg ; s = 5.4 N/mm = 5400 N/m

Since the force exerted by dashpot is 40 N, and the mass has a velocity of 1 m/s, therefore

Damping coefficient (actual),

c = 40 N/m/s

1. Critical damping coefficient,

we know that critical damping   coefficient,

2.  Damping factor, 

we know that damping factor,

c/c_c = 40/416 = 0.096

3.  Logarithmic decrement, 

we know that logarithmic decrement,

4.  Ratio of two consecutive amplitudes.

Let x_n and x_{n + 1} = Magnitude of two consecutive amplitudes,

we know that logarithmic decrement,