A mass is hung from a spring and set in motion so that it oscillates continually up and down. The velocity $v$ of the weight at time $t$ is given by the equation

with $v$ measured in feet per second and $t$ measured in seconds. Determine the maximum velocity of the mass and the amount of time it takes for the mass to move from its lowest position to its highest position.



The picture below illustrates this velocity over time. You can click on the picture for a larger version if desired.