question_answer

A damped oscillator attains the first amplitude of 500 mm after starting from rest. After 100 oscillations the amplitude remains 50 mm. The time period of motion is 2.3 sec. The damping coefficient well be:

A)  \[1\text{ }se{{c}^{-1}}\]              

B)  \[0.1\text{ }se{{c}^{-1}}\]

C)  \[0.01\text{ }se{{c}^{-1}}\]                        

D)  \[0.001\text{ }se{{c}^{-1}}\]

Correct Answer: C

Solution :

The amplitude of damped oscillation is \[a={{a}_{0}}{{e}^{-{{b}_{0}}t}}\] where \[{{b}_{0}}\] is damping factor after 100 oscillation