{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

s11_mthsc208_hw13

s11_mthsc208_hw13 - MthSc 208 Spring 2011(Differential...

This preview shows page 1. Sign up to view the full content.

MthSc 208, Spring 2011 (Differential Equations) Dr. Macauley HW 13 Due Friday March 18th, 2011 (1) Solve the following differential equations: (a) y 00 + 6 y 0 + 9 y = 5 (b) y 00 = - ω 2 y (c) y 0 + 2 y = e t (d) y 0 + 3 y = 0. (2) Find the Laplace transform of the following functions by explicitly computing Z 0 f ( t ) e - st dt . (a) f ( t ) = 3 (b) f ( t ) = e 3 t (c) f ( t ) = cos 2 t (d) f ( t ) = te 2 t (e) f ( t ) = e - 3 t sin 2 t (3) Sketch each of the following piecewise defined functions, and compute their Laplace trans- forms. (a) f ( t ) = 0 , 0 t < 4 5 , t 4 (b) f ( t ) = t, 0 t < 3 3 , t 3 (4) Engineers frequently use the Heavyside function , defined by H ( t ) = 0 , t < 0 1 , t 0 to emulate turning on a switch at a certain instance in time. Sketch the graph of the function x ( t ) = e 0 . 2 t and compute its Laplace transform, X ( s ). On a different set of axes, sketch the graph of y ( t ) = H ( t - 3) e 0 . 2 t and calculate its Laplace transform,
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online