Unformatted text preview: ! S2
9 10 Ex: Mechanical accelerometer Example: Newton’s law
M We want to know the trajectory of x(t). By Laplace transform,
x(t). (Total response) = (Forced response) + (Initial condition response) 11 12 Ex: Mechanical accelerometer (cont’d)
We would like to know how y(t) moves when unit
step f(t) is applied with zero ICs.
By Newton’s law
By Ex: Mechanical accelerometer (cont’d)
Suppose that b/M=3, k/M=2 and Ms=1.
Partial fraction expansion
Partial Inverse Laplace transform
Inverse 0 Amplitude -0.1 -0.2 -0.3 -0.4 -0.5
0 13 Summary & Exercises
Solution procedure to ODEs
1. Laplace transform
2. Partial fraction expansion
3. Inverse Laplace transform Next, modeling of physical systems using
Derive the solution to the accelerometer problem.
E2.4 in the textbook.
E2.4 15 2 4
e 8 10 14...
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- Spring '08