University of Illinois, Urbana Champaign
ME 340
ME 340 – Laviers
Section: Wed. 3pm
10/30/19
Pre-Lab 5
1.
2.
3.
4. Find the natural frequencies and mode shapes of a linear, time invariant mechanical system
-value problem: Is this periodic?
number
6. Suppose that an undamped, linear, time-invariant, two-degree-of-freedom mechanical system
has
...[Show More]
ME 340 – Laviers
Section: Wed. 3pm
10/30/19
Pre-Lab 5
1.
2.
3.
4. Find the natural frequencies and mode shapes of a linear, time invariant mechanical system
-value problem: Is this periodic?
number
6. Suppose that an undamped, linear, time-invariant, two-degree-of-freedom mechanical system
has a mode shape (-43) with corresponding natural frequency 2. Sketch the steady-state
response for the two degrees of freedom if the inputs f1(t) and f2(t) are both harmonic with
frequency 1.98 and there is small damping present.
c.
7. Consider a linear, time-invariant, two-degree-of-freedom mechanical system that has two
natural frequencies whose ratio is not a rational number. Suppose that a combination of
impulses f1(t) and f2(t) results in the response shown in the graph below. Use this to determine
one of the natural frequencies and the corresponding mode shape.
8. Consider the two-degree-of-freedom mechanical suspension, shown below, where x1 and x2
denote displacements of the lower and upper plate, respectively, relative to the undeformed
configuration of the two springs. Compute the natural frequencies and the corresponding mode
shapes.
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