MTE202 Study Guide - Final Guide: Oliver Heaviside, Heat Equation, Differential Form

• School: University of Waterloo
• Department: Mechatronics Engineering
• Course: MTE202
• Professor: Peter Teertstra

Document Summary

Use for solving functions that in include heaviside and/or dirac. Delta functions: use properties of laplace transform and ics to obtain. Take laplace transform of both sides equation in terms of the transform variable. Use for coupled spring-mass system: write equation in differential form using the. L3[x] + l4[y]=f2(t) x"-(cid:1007)(cid:454)+(cid:1008)(cid:455) l1=d-3 and l2=4. [l1 l 4- l 2 l 3]x = l 4[f1(t)] l 2[f2(t)] [l1 l 4- l 2 l 3]y = l 1[f2(t)] l 3[f1(t)] Sub back into original equation to solve for constants. In flow rate this is generally mass of a solute in a solution. Find the physical laws and relations that govern the problem. In flow rate problems this usually conservation of mass in the form: (cid:1856)(cid:1865)(cid:1856)(cid:1872)=(cid:1865)(cid:3041) (cid:1865)(cid:3042)(cid:3048)(cid:3047) (cid:1856)(cid:1876)(cid:1856)(cid:1872)=(cid:1832)(cid:3041)(cid:1829)(cid:3041) (cid:1832)(cid:3042)(cid:3048)(cid:3047)(cid:1876)(cid:4666)(cid:1872)(cid:4667)(cid:3042)(cid:3048)(cid:3047) Use for forced vibrations in a spring-mass system. Else us vop: use superposition to find y (y= yc+ yp, use ics to solve for remaining coefficients, use r to determine u1 and u2.