7.1 Given the input-output (I/O) equation 2y + 10y = 3u(t) Sketch the response y(t) for a step input u(t)=6U(t) and the initial condition y(0) = -2.

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A: given,open loop transfer functionG=ks(s+3)(s+3)

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A: Solution: Given Data:   To Find: State-space model of the system.

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Q: Figure 2). 1.2 1 0.8 Peak value: 1.1878 0.6 Peak time: 2.0723 sec 0.4 splacement of mass

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Q: 5. Calculate the response of the system below 27 -3 [ 8 1 ] * 0 + [2] 3³] × 0) = 0 (t) -3 given the…

A: Step 1: Step 2:

Q: R(s) K XIS s+5 s+2 s+3 Y(s)

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Q: 5. Afeedback system's open-loop transfer function is K G(s) = s(s+ 3)(s+ 6) 1)Sketch the system root…

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A: Given:The system model is given below;

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.