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A mass weighing 24 pounds stretches a spring 4 feet. The
Chapter 5, Problem 28E(choose chapter or problem)
A mass weighing 24 pounds stretches a spring 4 feet. The subsequent motion takes place in medium that offers a damping force numerically equal to \(\beta(\beta>0)\) times the instantaneous velocity. If the mass is initially released from the equilibrium position with an upward velocity of 2 ft/s, show that when \(\beta>3 \sqrt{2}\) the equation of motion is
\(x(t)=\frac{-3}{\sqrt{\beta^{2}-18}} e^{-2 \beta t / 3} \sinh \frac{2}{3} \sqrt{\beta^{2}-18} t\).
Text Transcription:
beta\beta>0
beta>3sqrt2
x(t)=frac-3sqrtbeta^2-18e^-2\betat/3\sinhfrac23sqrt\beta^2-18t
Questions & Answers
QUESTION:
A mass weighing 24 pounds stretches a spring 4 feet. The subsequent motion takes place in medium that offers a damping force numerically equal to \(\beta(\beta>0)\) times the instantaneous velocity. If the mass is initially released from the equilibrium position with an upward velocity of 2 ft/s, show that when \(\beta>3 \sqrt{2}\) the equation of motion is
\(x(t)=\frac{-3}{\sqrt{\beta^{2}-18}} e^{-2 \beta t / 3} \sinh \frac{2}{3} \sqrt{\beta^{2}-18} t\).
Text Transcription:
beta\beta>0
beta>3sqrt2
x(t)=frac-3sqrtbeta^2-18e^-2\betat/3\sinhfrac23sqrt\beta^2-18t
ANSWER:Step 1 of 4
In this problem, we need to show that when the equation of motion is