1) A 5 lb. weight hangs vertically on a spring whose spring constant k = 10. The weight is pulled 6 inches farther down and released. Find the equation of motion, its period and the frequency. What would the units be for k?
We have to keep in mind that British units are being used here so the acceleration of gravity, g = 32 ft/sec2 and the mass m is in slugs. The mass, recall is W/ g so that:
or: x” + 64 x = 32
2) For the circuit shown, consider the special case of NO capacitor. Then the differential equation of interest becomes:
L (dI/dt) + RI = E
It’s instructive to first solve this form where E is presumed constant. Begin by re-arranging the DE to get:
Let u = (E – RI) , Then: du = - RdI and dI = -du/ R