m238sp06t3 - Mathematics 238 test three due Friday, May 26,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mathematics 238 test three due Friday, May 26, 2006 1 . Given the initial value problem y 00 + 169 y = 0 and y (0) = 0 and y (0) = 1 find the solution function y ( t ) determine the amplitude and the period of the solution y ( t ). find the first two positive values at which y ( t ) attains a local maximum value. 2 . Given the initial value problem y 00 + 10 y + 169 y = 0 and y (0) = 0 and y (0) = 1 find the solution function y ( t ) determine the first two positive values at which y ( t ) attains a local maximum value calculate the quasi-period of the solution (the t-difference between locations of adjacent local maximum values) and the percentage decrease between adjacent maximum values. 3 . Use the variation of parameters technique to show that the solution to the initial value problem y 00 + 4 y = g ( t ) and y (0) = 0 and y (0) = 0 is given by the formula y ( t ) = 1 2 Z t- g ( s ) sin 2 s ds cos 2 t + 1 2 Z t g ( s ) cos 2 s ds sin 2 t Show that this formula is equivalent to the more concise...
View Full Document

Page1 / 2

m238sp06t3 - Mathematics 238 test three due Friday, May 26,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online