Key to Math 336 Old Test 3


1. -5/4 +1/20 e^{-4t} +6/5 e^t.

   e^{-2t} [cos(sqrt{7} t) -5/sqrt{7} sin(sqrt{7} t)].

   1/5 [1/(2sqrt{5}) sin(sqrt{5} t) -1/2 t cos(sqrt{5} t)].

2. -1/3 (t +1/3 -1/3 e^{3t}).

3. 2/s^3 -e^{-3s} (2/s^3 +6/s^2 +1/s) +e^{-7s} (5/s^2 +27/s).

4. 2.07 (Hz).

5. 7/5 u(t-3) [1 -cos(sqrt{5} (t-3))] -7/5 u(t-6) [1 -cos(sqrt{5} (t-6))]

   =0 if 0 <= t < 3,

    7/5 [1 -cos(sqrt{5} (t-3))] if 3 <= t < 6,

    7/5 [cos(sqrt{5} (t-6)) -cos(sqrt{5} (t-3))] if t >= 6.

6. x(t) =e^{-7t/2} (6 -5 t).

   1.2 (seconds).