Chapter 10.8, Problem 1TFR

For Questions (a)-(d), 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) The impulse of a force $F\left(t\right)$ acting on an object is obtained by integrating $F\left(t\right)$ over all values of $t$.

(b) A unit impulse force is a force that acts instantaneously and has unit impulse.

(c) The Laplace transform of the unit impulse function $\delta \left(t-a\right)$ is $e^{as}$.

(d) The initial-value problem governing the motion of a spring mass-system that is dealt an instantaneous blow at $t=a$ is a second order nonhonomogenous differential equation involving the unit impulse function.

(e) The instantaneous blow delivered to a spring-mass system determines the initial conditions for the nonhomogenous differential equation governing the motion of the mass as a function of time.