Energy Mass Spring System Given Sum Potential Energy Kinetic Energy Absence Damping Energy Q23371667
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The energy of the mass-spring system in given by the sum of the potential energy and kinetic energy. In absence of damping, the energy is conserved. (a) Plot the quantity E = 1/2 mv^2 + 1/2 ky^2 as a function of time. What do you observe? (pay close attention to the y-axis scale and, if necessary, use y1im to get a better graph). Does the graph confirm the fact that the energy is conserved? (b) Show analytically that dE/dt = 0. (Note that this proves that the energy is constant). (c) Plot u 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?Show transcribed image text The energy of the mass-spring system in given by the sum of the potential energy and kinetic energy. In absence of damping, the energy is conserved. (a) Plot the quantity E = 1/2 mv^2 + 1/2 ky^2 as a function of time. What do you observe? (pay close attention to the y-axis scale and, if necessary, use y1im to get a better graph). Does the graph confirm the fact that the energy is conserved? (b) Show analytically that dE/dt = 0. (Note that this proves that the energy is constant). (c) Plot u 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?