MT-1620 al.2002 Return to the simplest system the single spring-mass This is a one degree-of-freedom system with the governing equation mg t q F First consider Free Vibration Set f=o resulting in mq+kq=0 The solution to this is the homogeneous solution to the general equation For an Ordinary Differential Equation of this form, know that the solution is of the form g() mppt kepl=o =mp+k=0(in order to hold for all t Paul A Lagace @2001 Unit 20-2qt MIT - 16.20 Fall, 2002 Return to the simplest system: the single spring-mass… This is a one degree-of-freedom system with the governing equation: m q˙˙ + k q = F First consider… Free Vibration ⇒ Set F = 0 resulting in: m q˙˙ + k q = 0 The solution to this is the homogeneous solution to the general equation. For an Ordinary Differential Equation of this form, know that the solution is of the form: () = e pt ⇒ m p2e pt + k e pt = 0 ⇒ 2 mp + k = 0 (in order to hold for all t) Paul A. Lagace © 2001 Unit 20 - 2