MATH 255 Lecture Notes - Lecture 7: The Roots
Document Summary
We dealt with section 2. 6: forced oscillations and resonance this week. Consider a mass on a spring depicted by the second-order linear ode: mx. + kx = f (t); (1) where m is the mass, c is friction constant, k is spring constant, and f is the external force. In particular, we consider periodic forcing: f (t) = f0 cos(!t), where. R are amplitude and frequency of the external force respectively. It is convenient to write (1) as x. When there is no damping, c = 0, the equation reduces to x. The general solution for the associated homogeneous equation is xc(t) = c1 cos(!0t) + c2 sin(!0t): (2) (3) To (cid:12)nd a particular solution of (3), we try the function xp(t) = a cos(!t), since the right hand side of (3) is f0 m cos(!t). 0 cos(!t) is a particular solution of (3).
