A 48-kg mass, when attached to the end of a spring hanging vertically, stretches the spring 3 m. The mass is in a medium that exerts a viscous resistance of 912 N when the mass has a velocity of 3 m/sec. Assume the mass is given an initial velocity of 10 m/s from the equilibrium position. a) Determine the spring constant k. Use g = 10 m/sec. k=
b) Determine the damping coeffient 7. 7=
c) If the initial value problem for y(t), where y(t) denotes the displacement (in meters) of the mass from its equilibrium rest position, can be written in the form my'' + yy' + ky O where y(0) = yo and y'(0) = y'. what are the values of yo and y'o? Yo = yo
d) Solve it only far enough to describe the motion of the system with the terminology of this course. The system is e) What value of the damping coefficient y is required for the system to be critically damped? No decimals. Use "sqrt(foo)", without quotes, if you need the square root of foo. 7=