Energy of a Mass/Spring System

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A mass/spring system oscillates back and forth. The 20-kg block is attached to a spring of constant 10 N/m and rides on a frictionless floor. The distance grid is in meters and the times are shown in seconds. Study the graphs of the block's kinetic energy, the spring's potential energy, and the system's total energy as functions of time. How are they related?


  1. At any point in the block's motion, "measure" the kinetic and potential energies from the graphs. Can you verify that they are calculated correctly? (Use the Interactive Help to display the block's instantaneous velocity.)
  2. What should be true of the total energy? Why?


See Serway and Beichner, Physics For Scientists and Engineers 5th Edition, Section 8.1

Illustration written by Steve Mellema