261_pdfsam_math 54 differential equation solutions odd

261_pdfsam_math 54 differential equation solutions odd - +...

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

View Full Document Right Arrow Icon
Review Problems Also, the mass m of the weight is m = w g = 32 32 =1(s lug) , and the damping constant b = 2 lb-sec/ft. The external force is given to be F ( t )= F 0 cos γt with F 0 =4and γ =8. Clearly, we have an underdamped motion because b 2 4 mk =4 256 < 0. So, we can use formula (6) in Section 4.9 for the steady-state solution. This yields y p ( t )= F 0 ( k 2 ) 2 + b 2 γ 2 ± ( k 2 )cos γt + sin γt ² = 4 (64 8 2 ) 2
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: + 2 2 8 2 (64 8 2 ) cos 8 t + (2)(8) sin 8 t = 1 4 sin 8 t . The resonant frequency for the system is r / (2 ), where r is given in (15), Section 4.9. Applying this formula, we get resonant frequency = 1 2 r k m b 2 2 m 2 = 1 2 s 64 1 2 2 2(1 2 ) = 62 2 . 257...
View Full Document

Ask a homework question - tutors are online