Given a system defined by this differential equation:?

Question

f-K*x-D*(dx/dt) = M*(d^2x/dt^2)

where:

f = an external force, positive in the +x direction (an initial "impulse" of +100,000N for .0004 seconds)
x = displacement of mass M, in meters (initially stationary at x = 0)
K = a spring constant (15 N per meter)
D = a damping coefficient (40 N-second per meter)
M = a mass (80 kg)

Plot x as a function of time, showing how it varies as a result of the "impulse" Label the axes with appropriate dimensions and plot enough points to reveal the general behavior of x.

Answer 1

Your asking about the response of a damped system to an impulse. The answer depends on the specific parameters.

As usual, wikipedia is your friend:
http://en.wikipedia.org/wiki/Damping

In any case, it is clear that for the first .0004 seconds, both x and dx/dt increase. Then dx/dt starts decreasing and finally becoming negative. At that point x starts decreasing. That's when the degree of damping enters into things.