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Lecture Notes (3)

# S2 s2 s3 s3 9 10 ex mechanical accelerometer example

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Unformatted text preview: ! S2 S2 S3 S3 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 We 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. Suppose 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 Solution 1. Laplace transform 2. Partial fraction expansion 3. Inverse Laplace transform Next, modeling of physical systems using Next, Laplace transform Exercises Exercises Derive the solution to the accelerometer problem. Derive E2.4 in the textbook. E2.4 15 2 4 6 Tim [sec] e 8 10 14...
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