The the laplace transform of a function f(t), which is defined for all t≥0, is denoted by l{f(t)} and is defined by the improper integral l{f(t)}(s)=∫[infinity]0e−st⋅f(t)dt, as long as it converges. laplace transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (hint: think of ss as a fixed constant) 1. find l{t} (hint: remember integration by parts)

The force on a cutting tool are 2600n vertically downward and 2100 horizontal. determine the resultant force acting on the tool and the angle at which it acts.

Which of the following components of a pid controlled accumulates the error over time and responds to system error after the error has been accumulated? a)- proportional b)- derivative c)- integral d)- on/off.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.