A 0.5-kg mass is attached to a spring with spring constant 2.5N/m. The spring experiences friction, which acts as a forceopposite and proportional to the velocity, with magnitude 2 N forevery m/s of velocity. The spring is stretched 1 meter and thenreleased.
(a) Find a formula for the position of the mass as a function oftime.
(b) How much time does it take the mass to complete oneoscillation (to pass the equilibrium point, bounce back, and returntraveling in the same direction)? 1
(c) By what fraction has the amplitude of the motion decreasedin this time?
(d) Do the answers to (b) and (c) depend on the initial positionof the mass? Why or why not?
(e) By immersing the spring in one of a variety of rare,delicious syrups, it’s possible to increase the damping constantwhile keeping the spring constant the same. Can you increase thedamping constant so that the spring doesn’t oscillate at all, butjust returns to its starting point? What’s the smallest value ofthe damping constant that will do this?
