Question

Calculate logarithmic decrement if damping factor is 0.33
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Answer 1

2.19 is damping factor of 0.33

Answer 2

Given:

Damping factor is given as 0.33

To Find:

The logarithmic decrement if damping factor is 0.33

Solution:

Let, us consider damping factor be ε = 0.33 and logarithmic decrement be δ

We know that,

ε = $\bold{\frac{\delta^2}{\sqrt{4\pi^2+\delta^2}} }$    ......(1)

From the equation (1) we get

δ = $\bold{\frac{2\pi \varepsilon}{\sqrt{1-\varepsilon^2}} }$   ......(2)

Put the value of damping factor ε = 0.33 in equation (2)

δ = $\bold{\frac{2\pi \times 0.33}{\sqrt{1-(0.33)^2}} }$

Calculating the above equation we will get

δ = 2.19

∴ The required logarithmic decrement is 2.19 if damping factor is 0.33.