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2. The energy of the mass-spring system is given by the sum of the potential energy and kinetic energy. In absence of damping, the energy

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2. The energy of the mass-spring system is given by the sum of the potential energy and kinetic energy. In absence of damping, the energy is conserved (a) Add commands to LAB05ex1 to compute and plot the quantity E ^mu2 + ^ky as a function of time. What do you observe? (pay close attention to the y-axis scale and, if necessary, use ylim to get a better graph). Does the graph confirm the fact that the energy is conserved? (b) Show analytically that -0.(Note that this proves that the energy is constant) (c) Add commands to LAB05ex1 to plot v vs y (phase plot). Does the curve ever get close to the origin? Why or why not? What does that mean for the mass-spring system? Mass-Spring System with Damping When the movement of the mass is damped due to viscous effects (e.g., the mass moves in a cylinder containing oil, situation (d)), an additional term proportional to the velocity must be added. The resulting equation becomes dt dt dt 2. The energy of the mass-spring system is given by the sum of the potential energy and kinetic energy. In absence of damping, the energy is conserved (a) Add commands to LAB05ex1 to compute and plot the quantity E ^mu2 + ^ky as a function of time. What do you observe? (pay close attention to the y-axis scale and, if necessary, use ylim to get a better graph). Does the graph confirm the fact that the energy is conserved? (b) Show analytically that -0.(Note that this proves that the energy is constant) (c) Add commands to LAB05ex1 to plot v vs y (phase plot). Does the curve ever get close to the origin? Why or why not? What does that mean for the mass-spring system? Mass-Spring System with Damping When the movement of the mass is damped due to viscous effects (e.g., the mass moves in a cylinder containing oil, situation (d)), an additional term proportional to the velocity must be added. The resulting equation becomes dt dt dt

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