A 10 kilogram object suspended from the end of a vertically hanging spring stretches thespring 9.8 centimeters. At time t = 0, the resulting mass-spring system is disturbed from its reststate by the force F(t) = 80 cos(8t). The force F(t) is expressed in Newtons and is positive inthe downward direction, and time is measured in seconds.a. Determine the spring constant k.k= 1000Newtons / meterb. Formulate the initial value problem for y(t), where y(t) is the displacement of the objectfrom its equilibrium rest state, measured positive in the downward direction. (Give youranswer in terms of y, y' , y ", t.)Differential equation: 10y"+1000y=80cos(8t)help (equations)Initial conditions: y(0) = 0and y'(0)help (numbers)c. Solve the initial value problem for y(t).y(t) =help (formulas)d. Plot the solution and determine the maximum excursion from equilibrium made by the objecton the time interval 0

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