ENG 6 Lecture Notes - Lecture 19: Periodic Function, Simple Harmonic Motion
Document Summary
Some differential eq. s can be solved analytically, many others need to be solved numerically, with a computer method. Graphical solution is not necessarily less rigorous than an analytical one. Assign a new variable equal to original variable, rewrite derivative of new variable, use that to rewrite second derivative. Use function: ode45: arguments: function handle. A vector representing initial and final times of solution; Allows you to solve for constants as well: returns a vector of time points and a matrix with columns corresponding to value of each variable at those times. Mass, resting on one surface, is connected to a wall by a spring and sliding along the surface. Nonlinear differential equations: population growth, numerical solutions can address more problems than just linear, time-independent diff. eqs, dp/dt is nonchanging, but once p = k, it becomes zero and the population stops growing. Time varying carrying capacity: varies periodically btwn min and max.
