ENGR-25_HW-01_Solution.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 25 Chp8 Tutorial: Prob 8.28 Solution

ENGR-25_HW-01_Solution.ppt 2 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Errata UNITS WRONG  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 ω p, ω c → rads/sec (r/s)

ENGR-25_HW-01_Solution.ppt 3 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods The situation  Given a Frictionless Mass- Spring System Characterized by the ODE  With 0 th & 1 st order I.C.’s  Find y(t) for ω p = 1, 5.1, 10 r/s

ENGR-25_HW-01_Solution.ppt 4 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

ENGR-25_HW-01_Solution.ppt 5 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

ENGR-25_HW-01_Solution.ppt 6 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

ENGR-25_HW-01_Solution.ppt 7 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

ENGR-25_HW-01_Solution.ppt 8 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

ENGR-25_HW-01_Solution.ppt 9 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods P8.28 Analytical Soln

ENGR-25_HW-01_Solution.ppt 10 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods P8.28 Analytical Plot

ENGR-25_HW-01_Solution.ppt 11 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

ENGR-25_HW-01_Solution.ppt 12 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

ENGR-25_HW-01_Solution.ppt 13 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods P8.28 Numerical Soln  The Function file for the ODE Solver Call

ENGR-25_HW-01_Solution.ppt 14 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods P8.28 Numerical Soln

ENGR-25_HW-01_Solution.ppt 15 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Case-a: ω p = 1 rad/sec

ENGR-25_HW-01_Solution.ppt 16 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Case-b: ω p = 5.1 rad/sec

ENGR-25_HW-01_Solution.ppt 17 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Case-c: ω p = 10 rad/sec

ENGR-25_HW-01_Solution.ppt 18 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Case-b: 100 sec  Note the “beating” with a Period of about 63 sec