Hello,
You asked for the value of logarithmic decrement if damping factor is 0.33.
Look, The logarithmic decrement represents the rate at which the amplitude of free damped vibration decreases. It is defined as the natural log of the ratio of any two successive amplitudes. It is found from the time response of underdamped vibration (oscilloscope/ real-time analyzer).
So, 2.19 is the logarithmic decrement value for this question.
Hope this helps!!
Question : The value of $\frac{(0.67 \:\times\: 0.67 \:\times\: 0.67)\:-\:(0.33 \:\times\: 0.33 \:\times\: 0.33)}{(0.67 \:\times\: 0.67)\:+\:(0.67 \:\times\: 0.33)\:+\: (0.33 \:\times\: 0.33)}$ is:
Option 1: 11
Option 2: 1.1
Option 3: 3.4
Option 4: 0.34
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