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A body of mass 4 gr attached to a vertical spring stretches it 160 cm to reach the equilibrium position. Approximate the acceleration of gravity by g=1000 cm/sec², and neglect any air resistance.

a) Find a differential equation of the form y=F(y,y) for the displacement function y from the equilibrium position, with ypositive downwards. Use yp to denote de derivative y.

F(y,y)=

b) At t₀=0 sec the body is pushed up an additional 2 cm and then released with an initial velocity of 5(3^1/2) cm/sec. Find the solution y of the equation in part (a), and also provide the amplitude A and the phase-shift in the interval (,].

y(t) =

A=

=

Please explain.