A10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. at time t=0, the resulting mass-spring system is disturbed from its rest state by the force f(t)=80cos(8t). the force f(t) is expressed in newtons and is positive in the downward direction, and time is measured in seconds.

a. determine the spring constant k.
b. formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction.