Suppose a 64-Lb Object Stretches a Spring 2 Feet While $\alpha$

Short Answer

Suppose a 64-lb object stretches a spring 2 feet while in equilibrium, and a dashpot provides a damping force of 3 lbs for every foot per second of velocity. The form of the equation of unforced motion of the object in such a spring-mass system is where m is the mass of the object, c is the damping constant, and k is the spring constant. Assume that the spring starts at a height of 5/2 feet below the horizontal with an upward velocity of - 3/2 feet per second.
For what values of $\alpha$ and $\beta$ is the function the general solution of the equation of motion for this spring-mass system? Provide exact values, not decimal approximations.
$\alpha$ = _______________, $\beta$ = _______________