Quiz 7 solutions

# Quiz 7 solutions - Name Quiz 7(30 pts 1 Sketch a sinusoid...

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Name______________________ Quiz 7 1. Sketch a sinusoid with amplitude A = 3.0 and frequency ω = 1.0, as well as the steady state time response of a first order system with τ = 3.0 sec and K = 1.0 to this sinusoidal input; plot the curves versus ω t. Make sure your sketch shows the amplitudes reasonably correctly. Recall that at steady state: () 1 2 1 KA y( t ) sin t tan ω ωτ =− + . We need to find the amplitude and phase of the response. ωτ = 3 1. estimation method 2 1 1 M( ) = + 2 11 1 1 1 90 3 3 3 19 1 0 9 113 M . * == = = = + + The amplitude is reduced by a factor of 3. At ωτ = 1, φ = -45°. At ωτ = 10, φ = -90°. The delay is between 45° and 90°. On a log scale, one can make a straight line approximation (see below) for the phase shift

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Quiz 7 solutions - Name Quiz 7(30 pts 1 Sketch a sinusoid...

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