Consider a cylindrical sample of rubber, fixed at one end. It may be characterised by four state variables, but we are interested in only two, namely, temperature T (in K) and length L (in cm), the latter being varied through the application of some tensile/compressive force F. I It can be shown that, under certain conditions, T and L are related via the 1st order ODE dT dL T 10 (2-2-²) This equation assumes that the relaxed length of the cylinder is 1 cm i.e. L < 1 implies compression, while L> 1 implies extension,

Find the m

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 90t, at which time the fuel is exhausted and it becomes a freely "falling" body. Eighteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -11 ft/s in 5 seconds. The rocket then "floats" to the ground at that rate. (a) Determine the position function s and the velocity function v (for all times t). 4512 if 0 sts 3 405 if 3 26 15r3 if 0 sts 3 405 if 3 26

A large tank is filled to capacity with 600 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds salt in the tank at time t.