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with a complete solution A body of mass 2 gr attached to a vertical spring stretches...

with a complete solution

A body of mass 2 gr attached to a vertical spring stretches it 1000/4 cm to reach an equilibrium position. When the body moves in the air it experiences a resistance opposite to its movement, proportional to its speed, with a damping constant d = 10 gr/sec. Approximate the acceleration of gravity by g = 1000 c m / s e c 2 . b. Find a differential equation of the form y ′′ = F ( y , y ′ ) for the displacement function y from the equilibrium position, with y positive downwards. Use yp to denote de derivative y ′ . F ( y , y ′ ) = -4y - 5yp d. At t 0 = 0 sec the body is pushed up an additional 4 cm and then released with an initial velocity of 2 cm/sec. Find the solution y of the equation in part (b). y(t) = _____

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