a) A spring attached to a ceiling is stretched 1.96 m by a 4 kg mass. Find the H

Question

a) A spring attached to a ceiling is stretched 1.96 m by a 4 kg mass. Find the Hooke's Law spring constant k. (9.8m/sec = acc. due to grav)

b) If the mass is set into motion in a medium that imparts a damping force equal to 16 times the velocity, find the diff. eq. for the position, x(t), of the mass as a function of time.

c) Solve the DE from part b.

d) Determine the eq. of motion if the mass is initially released from a postion .5(m) below equilibrium with a nupward velocity of 1.866*(m/s)*(((sqrt(3)+2)*m)/(2s)) ...

e) Identify the period, phase shift, phase angle, frequency, and initial amplitude.

I know its a lot, but I dont know what to do whatsoever. Will reward maximum points. Thanks

Explanation / Answer

a) k = mg/x = 4*9.8/1.96 = 20 N/m

b) 4y'' + 16y' + 20y = 0

c) y' + 4y' + 5y = 0, r^2 + 4r + 5 = (r + 2)^2 + 1 =0, so r = -2

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