A spring with spring constant 11.5 N/m hangs from the ceiling. A 490 g ball is attached to the spring and allowed to come to rest. It is then pulled down 6.70 cm and released. What is the time constant if the ball's amplitude has decreased to 2.20 cm after 30.0 oscillations?

The time constant is    

Explanation:

From the question we are told that

   The spring constant is  

   The mass  of the ball is  

   The amplitude of the  oscillation t the beginning is

    The amplitude after time t is  

    The number of oscillation is

Generally the time taken to attain the second amplitude is mathematically represented as

                                                   Here  T is the period of oscillation

=>    

=>    

Generally the amplitude at time t is mathematically represented as

Here a is the damping  constant so

 at   ,  

So  

=>  

taking natural log of both sides

=>      

=>  

Generally the time constant is mathematically represented as

=>    

=>    

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