A10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. at time t0, the resulting mass-spring system is disturbed from its rest state by the force f(t) 180 cos(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 k= newtons/meter 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. (give your answer in terms or y. y',y", t. differential equation: initial conditions: y(0) (equations) and y'(0) = (numbers) c. solve the intial value problem tor y(t) g(t) (formulas) d plot the solution and determine the maximum excursion rrom equilibrium made by the ob ect on the time interval ãooi there is no such maximum, enter none. maximum excursion meter