Question

A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences friction, which acts as a force opposite and proportional to the velocity, with magnitude 2 N for every m/s of velocity. The spring is stretched 1 meter and then released.

(a) Find a formula for the position of the mass as a function of time.

(b) How much time does it take the mass to complete one oscillation (to pass the equilibrium point, bounce back, and return travelling in the same direction)?

(c) By what fraction has the amplitude of the motion decreased in this time?

(d) Do the answers to (b) and (c) depend on the initial position of 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 constant while keeping the spring constant the same. Can you increase the damping constant so that the spring doesn’t oscillate at all, but just returns to its starting point? What’s the smallest value of the damping constant that will do this?

PLEASE SHOW YOUR DETAILED WORK.

Answer 1

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