Differential Equations and Matrix Algebra II (MA 222), Winter Quarter, 2002—2003
Quiz 7
NAME:
(5 pts) 1. Use Laplace transforms to solve x0 − 3x = 4δ(t − 2), x(0) = 0. Do this problem by hand.
(5 pts) 2. If f (t) = 2 and g(t) = sin(t), find f ∗ g(t) by hand. You may use g ∗ f if it’s more convenient.
(10 pts) 3. Assume that a spring mass system is set up in such a way that it is hanging from the
ceiling. Also assume that you are using the coordinate axis with 0 at equilibrium and
positive is downward. Given that m = 2, c = 3, k = 2, x(0) = 1, x0(0) = 1, and the only
external force is an impulse of 4 at time t = 1 (in the downward direction), what are the
position and velocity of the mass at time t = 2?
(10 pts) 4. A 200 gallon tank of brine initially contains 40 pounds of salt. Assume a brine solution
(containing 1/2 lb of salt per gallon) enters the tank at the rate of 6 gallons per minute and
the mixture leaves at the same rate. How much salt should you dump in after 1 hour (i.e.
at time t=60) so that at time t = 100, there are 120 pounds of salt in the tank?