The drawing to the left shows a mass m= 1.5 kg hanging from a spring with spring constant k = 10 N/m. The mass is also attached to a paddle which is emersed in a tank of water with a total depth of 33 cm. When the mass oscillates, the paddle acts as a damping force given by -b(dx/dt) where b= 260 g/sec. Suppose the mass is pulled down a distance 1.2 cm and released.
a) What is the time required for the amplitude of the resulting oscillations to fall to one third of its initial value?
b) How many oscillations are made by the block in this time?