261_pdfsam_math 54 differential equation solutions odd

# 261_pdfsam_math 54 differential equation solutions odd - 2...

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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
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Unformatted text preview: + 2 2 8 2 ± (64 − 8 2 ) cos 8 t + (2)(8) sin 8 t ² = 1 4 sin 8 t . The resonant frequency for the system is γ r / (2 π ), where γ r is given in (15), Section 4.9. Applying this formula, we get resonant frequency = 1 2 π r k m − b 2 2 m 2 = 1 2 π s 64 1 − 2 2 2(1 2 ) = √ 62 2 π . 257...
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## This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.

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