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Correct Units for ODE Analysis: Mass-Spring System

Analyze a mass-spring system's ODE with proper units. Find y(t) for different angular frequencies. Includes analytical and numerical solutions.

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Correct Units for ODE Analysis: Mass-Spring System

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  1. Engineering 25 Chp8Tutorial: Prob 8.28Solution Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. Errata • The subsequent numerical analysis is CORRECT, but some of the UNITS are WRONG. • The Correct Units • y(t) → meters • dy/dt → meters/second (m/s) • m → kg • k → Newtons/meter (N/m) • M → Newtons • K, B → meters • ωp , ωc → rads/sec (r/s)

  3. The situation • Given a Frictionless Mass-Spring System Characterized by the ODE • With 0th & 1st order I.C.’s • Find y(t) for ωp = 1, 5.1, 10 r/s

  4. P8.28 Analytical Soln

  5. P8.28 Analytical Plot

  6. P8.28 Numerical Soln • The Function file for the ODE Solver Call

  7. P8.28 Numerical Soln

  8. Case-a: ωp = 1 rad/sec

  9. Case-b: ωp = 5.1 rad/sec

  10. Case-c: ωp = 10 rad/sec

  11. Case-b: 100 sec • Note the “beating” with a Period of about 63 sec

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