The characteristic equation of a de motor control system can be approximated as 0.02] s³ + (1+0.1J)s² + 116.84s + 1843 = 0 Where the load inertia, JL, is considered as a variable parameter. Plot the root locus graph using MATLAB for variable JL ≥0. Show grid lines for damping ratio with steps of 0.1 and natural frequency up to 200 rad/sec with steps of 10 rad/sec. At what gain the system becomes unstable? Tabulate the gain versus poles in the root locus for the gain range where the system is stable. Use steps of 0.1 for the gain. Find the largest damped frequency of the system and the corresponding inertia load, JL for that frequency from the root locus graph or tabulated data. Find the inertia load, JL of the system such that is satisfies the 1% settling time requirement of 1.93 seconds.

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Find the Frequency Ratio, Displacement, Transmissibility Ratio, Absolute displacement of the mass, Type of Damping, and Equation of motion x(t). Assume Initial conditions for displacement and velocity. Graph 2 cycles of the vibrating system.

Help me with this ASAP. Thank you! Find the Following: 1. Natural angular velocity 2.Damped angular velocity 3. Equation of motion x(t). Assume Initial conditions for displacement and velocity 4. Graph 2 cycles of the vibrating system. You can use third party app for this.

5 Problem Match the following two frequency response diagrams: -0 0.4 |G(i w)| 0.2 10 |G(i w)| 5 Response A 2 3 4 5 6 7 8 Frequency, (rad/s) Response B 5 6 7 8 Frequency, w(rad/s) 1 2 3 4 6 6 10 10 10 to two of the following ODES 1. +x+100x = u(t) 5. +100x = u(t) 9. +100x = u(t) 3. x+x+5x= u(t) 4. x+x+x= u(t) 2. x+x+25x = u(t) : 6. x + 25xu(t) 10. +25x = u(t) 7. x+5x= u(t) 8. u(t) 11. +5x= u(t) = 12. xu(t)

solve, show solution and show matlab code for part b, vibrations

solve both and show matlab code   auto controls

1 Free Vibration Response of Single Degree of Freedom System(100 %) Figure 1 represent a simple vibration system. The free vibration response of an undamped single degree of freedom (SDOF) oscillator is given by its displacement x(t) satisfying x(t) = x(0)sin*(wt)e-2dwt + v(0) (1) -cos(wt)e-10dwt %3D where t is time in seconds and w = Vis the natural frequency of the system with m and k being the mass and the stiffness of the system. d is the damping coefficient of the system. Define v(t) and a(t) as the time dependent velocity and acceleration of the system. Write an M-file script using functions that will compute and plot 1. The displacement of the system x(t) over time 2. The velocity of the system v(t) over time 3. The acceleration of the system a(t) over time for three damping coefficients (d = 0,1,5) within a time interval 0 < t < 10 s. You will need THREE(3) functions, one for each displacement, velocity and acceleration calculations. Assume m = 10, k = 1 and that r(0) = v(0) =…

1. Consider the equation of motion of a single degree of freedom with the forcing function as shown below. 3x (t) + 12x (t) = 3 cos wt Compute the natural frequency and total response of the system, i.e., solution to the equation of motion, if the driving frequency is 2.5 [rad/sec] and the initial conditions are both zero.

1 Problem 5 4 State, x(t) SAWNO-Nw. ● ● Case 1 O 2 6 Time, sec. underdamped critically damped State, x(t) • overdamped 54321 ONS TY Case 2 2 ▷ Time, sec. 8 10 State, x(t) 5 2 + 3 4 Case 3 2 ▷ 6 Time, sec. 5432 State, x(t) & A & No. 2 Match each of the resposes above to one of the following second-order system types: • undamped Case 4 ▷ Time, sec.