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an 10 kg object is hung from a spring attached to a fixed support. The spring...

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Physics

an 10 kg object is hung from a spring attached to a fixedsupport. The spring constant of the spring is k=40 Nm**(-1) (I meanto the power of -1) Suppose an external downward force of magnitudef(T) = 20 e **(-2t) N is applied to the object, and damping due toair resistence occurs with damping constant beta = 40 N s m **(-1).Let y(t) denote the distance in meters of the object below itsequilibrium position at time t seconds. Take the gravitationalconstant to be g=9.8 m.s**(-2). a) Draw a diagram of the system,showing all forces acting on the object, assuming object is abovethe equilibrium position and moving down. Include the direction andmagnitude of each force.

b) state the equation of motion of object.

c) Find the general solution to the equation of motion.

d) Assume that the object initially starts at the equilibriumposition with the velocity of 2 m.s**(-1) upwards

i. Find the position of the object at any time.

ii. At what times, if any, is the object located at itsequilibrium position?

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