HW3_Assg - single degree of freedom oscillator are shown in Figure 2 and Figure 3 Estimate the damping ratio natural frequency ω n mass m

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Mechanical Vibrations Homework #3 Due: 27Sep04 - Start of Class Part 1: Work the following problems 1. Because you are a true explorer, you decide to add two springs and dampers to a single mass (see Figure 1). The parameters for the system are: ( m = 3 kg), ( k 1 = 100 N/m), ( k 2 = 200 N/m), ( c 1 = 1 Nm/s), ( c 2 = 2 Nm/s). a) Develop the equation of motion for the system in terms of the parameters show in Figure 1. b) Solve for the displacement of the system and plot the results for the following initial conditions x (0) = 1, ˙ x (0) = 5. c) Plot the transfer function ( H (Ω)) for the new | X (Ω) | . Assume the harmonic forcing is: f ( t ) = 600 cos Ω t Newtons. k 1 c 1 x(t) f(t) m k 2 c 2 Figure 1: Single degree of freedom system. 1
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2. The transfer function, amplitude of the steady-state response, and the transient response of a
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Unformatted text preview: single degree of freedom oscillator are shown in Figure 2 and Figure 3. Estimate the damping ratio ( ζ ), natural frequency ( ω n ), mass ( m ), viscous damping coefficient c , and stiffness ( k ) of the system from the graphs. 200 400 600 800 1000 1200-3-2-1 1 2 3 x 10-5 Transfer Function frequency [Hz] Real H( Ω ) [m/N] 200 400 600 800 1000 1200-5-4-3-2-1 x 10-5 frequency [Hz] Imag H( Figure 2: Single degree of freedom system transfer function. 2 200 400 600 800 1000 1200 1 2 3 4 5 x 10-3 Response Amplitude frequency [Hz] |X( Ω )| [m/N] 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-0.1-0.05 0.05 0.1 time [s] X h (t) Figure 3: Single degree of freedom steady-state response amplitude and transient response. 3...
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This note was uploaded on 08/22/2011 for the course EML 4220 taught by Professor Chen during the Spring '08 term at University of Florida.

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HW3_Assg - single degree of freedom oscillator are shown in Figure 2 and Figure 3 Estimate the damping ratio natural frequency ω n mass m

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