11. (a) A spring is stretched 10 cm by a force of 3 newtons (N). A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 N when the velocity of the mass is 5 m/s. If the mass is pulled down 5 cm below its equilibrium position and given an initial downward velocity of 10 cm/s, determine its position y at any time t. Find the quasi-frequency and the ratio of to the natural frequency of the corresponding undamped motion. (b) Draw a phase portrait of the equivalent dynamical system that includes the trajectory corresponding to the initial value problem in part (a).
11. (a) A spring is stretched 10 cm by a force of 3 newtons (N). A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 N when the velocity of the mass is 5 m/s. If the mass is pulled down 5 cm below its equilibrium position and given an initial downward velocity of 10 cm/s, determine its position y at any time t. Find the quasi-frequency and the ratio of to the natural frequency of the corresponding undamped motion. (b) Draw a phase portrait of the equivalent dynamical system that includes the trajectory corresponding to the initial value problem in part (a).
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Transcribed Image Text:11. (a) A spring is stretched 10 cm by a force of 3 newtons (N). A mass of 2 kg is hung from the spring and is
also attached to a viscous damper that exerts a force of 3 N when the velocity of the mass is 5 m/s. If the mass is
pulled down 5 cm below its equilibrium position and given an initial downward velocity of 10 cm/s, determine its
position y at any time t. Find the quasi-frequency and the ratio of to the natural frequency of the corresponding
undamped motion.
(b) Draw a phase portrait of the equivalent dynamical system that includes the trajectory corresponding to the
initial value problem in part (a).
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