A damped oscillator is formed by attaching a mass with m = 1.5kg to one end of a spring with spring constant k = 8 N/m. The otherend of the spring is anchored and the mass can slide on ahorizontal surface The damping force is given by –bv with b = 230g/s. At t=0, the mass is displaced so that the spring is compressedby 12 cm from its unstretched length and released from rest.
(a) Find the time required for the amplitude of the resultingoscillations to decay to 1/3 of its initial value.
(b) How many oscillations are made by the mass during thistime?
(c) Find the value of b so that the oscillator is criticallydamped.
(d) At t=0, this critically damped oscillator is displaced sothat the spring is stretched a distance of 12 cm beyond itsunstretched length, find the time required for mass to reach theposition for which the spring is stretched by only 4 cm.
