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A 10 10 kilogram object suspended from the end of a vertically hanging spring stretches the...

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Advance Math

A 10 10 kilogram object suspended from the end of a verticallyhanging spring stretches the spring 9.8 9.8 centimeters. At time?=0 t = 0 , the resulting mass-spring system is disturbed from itsrest state by the force ?(?)=70cos(8?) F ( t ) = 70 cos ( 8 t ) .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 ?.

b) Formulate the initial value problem for ?(?)y(t), where?(?)y(t) is the displacement of the object from its equilibriumrest state, measured positive in the downward direction. (Give youranswer in terms of ?,??,???,?y,y?,y??,t.)

c) Solve the initial value problem for ?(?)y(t).

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