Consider an spring-and-mass oscillator such as that of fig. 3.1, the top of whose spring is moved up and down with an amplitude s(t) = a cos omega t. set up the equation of motion for this system, and show that the steady-state solution for the displacement z(t) for the weight at the end of the spring is z(t)= alpha omega^2_0 squareroot (omega^2- omega^2_0)^2+omega^2 gamma^2 cos(omega t- empty set).