Amass of 4 kg stretches a spring 40 cm. the mass is acted on by an external force of f(t) = 97 cos(0.5t) n and moves in a medium that imparts a viscous force of 4 n when the speed of the mass is 8 cm/s. if the mass is set in motion from its equilibrium position with an initial velocity of 6 cm/s, formulate the initial value problem describing the motion of the mass. note that the acceleration due to gravity, g, is g = 980 cm/s2 find the general solution to your differential equation from the previous part. use c1 and c2 to denote arbitrary constants. use t for independent variable to represent the time elapsed in seconds. ea-(1/16) c1"sin(sqrt(6271/4)/8 t) e^-(1/16)"c2"cos(sqrt(6271/4)/8 "t) solve the differential equation with initial conditions describing the motion/the displacement y(t) of the mass from its equilibrium position.