Oscillations question

[guru]

A spring with spring constant 11 N/m hangs from the ceiling. A .540kg ball is attached to the spring and allowed to come to rest. It is then pulled down 6.2cm and released.
I need to find the time constant if the ball's amplitude has decreased to 2.8cm after 31 oscillations.

I need help on how to approach this problem

[Integral]

You have all the information you need to find the period of oscillation, do that. You also should have the governing equation for damped oscillatory motion. You know the amplitude of motion at 2 different times. Use that information to find your damping coefficient.

If you have more questions, please share with us what you have as for the equation of motion of a damped oscillator.