MAE 340 Lecture Notes - Lecture 7: List Of Trigonometric Identities, Step Response, Ramp Function

• School: University at Buffalo
• Department: Mechanical & Aerospace Engr
• Course: MAE 340
• Professor: J.Mook

Document Summary

Find the complete solution for the system with the lti ode. X + 2 x + 10x = f (t), x(0) = x(0) = 0 where the input f (t) is given by the sequential forcing: Compare the solution to the step response for a step input with an amplitude of 3: 0 f (t) = fstep(t) = (cid:26) 0. Often it is undesirable (or just unrealistic) to have an input that jumps suddenly from 0 to some non-zero value without any elapsed time or transition region. One way to get around this is to have a ramp that starts at zero and goes to the desired value within some speci ed time. However, the ramp function will have sudden jumps (discontinuities) in its rst derivative, which may also be unwanted. One possible alternative is to use a segment of a sinusoid to transition between two levels, as shown in this example.