A 10 kilogram object suspended from the end of a vertically hanging spring stretchesthe spring 9.8 centimeters. At time t = 0, the resulting mass-spring system isdisturbed from its rest state by the force F(t) = 50 cos(10t). The force F(t) isexpressed in Newtons and is positive in the downward direction, and time is measuredin 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 theobject from its equilibrium rest state, measured positive in the downwarddirection. (Give your answer in terms of y, y', y", t.)Differential equation:(equations)Initial conditions: y(0)= 0and y'(0)c. Solve the initial value problem for y(t).y(t) == 0helphelp (numbers)help (formulas)d. Plot the solution and determine the maximum excursion from equilibrium madeby the object on the time interval 0 ≤ t < ∞. If there is no such maximum, enterNONE.maximum excursion =meters help (numbers)

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