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

an 10 kg object is hung from a spring attached to a fixed support. The spring constant of the spring is k=40 Nm**(-1) (I mean to the power of -1) Suppose an external downward force of magnitude f(T) = 20 e **(-2t) N is applied to the object, and damping due to air resistence occurs with damping constant beta = 40 N s m **(-1). Let y(t) denote the distance in meters of the object below its equilibrium position at time t seconds. Take the gravitational constant 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 above the equilibrium position and moving down. Include the direction and magnitude 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 equilibrium position 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 its equilibrium position?

Expert Solution

genius_generous answered 2 years ago

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