A satellite controls its rotational velocity by extending an arm much like a balle- rina in a spin or a figure skater. Changing the length, L, of the arm changes the inertia of the satellite. The transfer function between the rotational velocity, w(s), and the incremental change in L, called AL(s) is given as w(s) AL(s) 2(s+4) (s +5) (s + 1)² The change in length is given as 1 AL(s) == S (4) (5) Determine the response to the change in length of the satellite's angular veloc- ity, w(t), in the time domain using partial fractions.

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transfer function from the image

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The ratio of the output voltage phasor to the input voltage phasor is called a transfer function. True False

Given the complex number in an algebraic form: 6.6 + j*1.2, what is the modulus of this number? 6.708 what is the angle of this number in radians? 0.1170

(b) Given the signal x(t) in Figure 3, sketch the signal for x(-2t-2): 2.5. 2 1.5 0.5 -0.5 0.5 1.5 2.5 3.5 Figure 3 Note: Show each step

Using the Routh-Hurwitz criterion, how many poles are in the right half-plane, the left half-plane, and on the jw-axis for the following system? ( R(S) s²-300s + 15 2s4 +353 + 16s2 + 15s + 30 C(s)

IN A SERIES RLC CIRCUIT DRIVEN BY SINUSOIDAL INPUT SIGNAL, THE PHASE BETWEEN THE CURRENT AND THE INPUT VOLTAGE IS PLOTTED IN THE NEXT GRAPH. When the frequency f = 60 kHz the phase (in radians) between the voltage on the capacitor and the voltage on the inductor is about: 1.6 1.2 0.8 0.4 -0.4 -0.8 -1.2 -1.6 1 10 100 1000 Frequency (f), kHz O a. zero O b. -1.57 O c. 0.003 O d. 1.57 O e. 3.14 Phase (0 ), rad