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Find the motion of the mass-spring system in the figure below with mass 0.125 kg damping 0, spring constant 1.125 kg/sec², and driving force cost-4 sint newtons, assuming zero initial displacement and velocity. Calculate the frequency of the driving force that would get you resonance to three decimal places.

Find the motion of the mass-spring system in the figure below with mass 0.125 kg damping 0, spring constant 1.125 kg/sec², and driving force cost-4 sint newtons, assuming zero initial displacement and velocity. Calculate the frequency of the driving force that would get you resonance to three decimal places.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the motion of the mass-spring system in the figure below with mass 0.125 kg damping 0, spring constant 1.125 kg/sec², and driving force cost-4 sint newtons, assuming zero initial displacement and velocity. Calculate the frequency of the driving force that would get you resonance to three decimal places.
Transcribed Image Text:Find the motion of the mass-spring system in the figure below with mass 0.125 kg damping 0, spring constant 1.125 kg/sec², and driving force cost-4 sint newtons, assuming zero initial displacement and velocity. Calculate the frequency of the driving force that would get you resonance to three decimal places.
The equation is thus, 0.125y" + 1.125y = cost - 4 sint; y" +9y = 8 cos t - 32 sin t. The solution satisfying the initial conditions is y = - cos 3t+ sin 3t+cost - 4 sin t, as obtained by the method of undetermined coefficients. The last two terms result from the driving force. In the first two terms, wo = √k/m = 3. This shows that resonance would occur if the driving force had the frequency w(2T) = 3/(2T).
Transcribed Image Text:The equation is thus, 0.125y" + 1.125y = cost - 4 sint; y" +9y = 8 cos t - 32 sin t. The solution satisfying the initial conditions is y = - cos 3t+ sin 3t+cost - 4 sin t, as obtained by the method of undetermined coefficients. The last two terms result from the driving force. In the first two terms, wo = √k/m = 3. This shows that resonance would occur if the driving force had the frequency w(2T) = 3/(2T).
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