Chapter 9.7, Problem 1TFR

True-False Review

For Questions (a)-(e), decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem in fact from the text. If false, provide an example, illustration, or brief explanation of why the statement is false.

(a) A coupled spring-mass system consisting of two masses and two springs can be solved as a first-order linear system $x^{\prime }=Ax$, where $A$ is a $2\times 2$ matrix whose entries are determined by the masses and spring constants.

(b) The units of the spring constant in the metric system are Newtons per meter.

(c) In the metric system, the concentration of chemical in a tank of solution is measured in grams.

(d) In a chemical mixing problem involving two tanks, the rate at which the fluid moves from tank $1$ to tank $2$ must be the same as the rate at which fluid moves from tank $2$ to tank $1$.

(e) In a chemical mixing problem with two tanks in which no solution flows in or out of the system from the outside and the rates of flow between the two tanks $r_{12}$ and $r_{21}$ are equal, the amount of chemical in each tank remains constant over time, regardless of the initial conditions.