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a) Given a critically damped system, find an analytical expression for the time when the response...
Find the analytical solution for the response of the following viscously damped 1 DOF system subjected to a force F(t)=Fcos(wt) Governing equation: mx(double dot) + cx(dot) + kx = F(t) w = 1 rad/sec Fo = 3 to= 0 m= 1kg c = 0.125 kg/s k = 1 N/m initial conditions: x0 = 2, x(dot)o = 0 Time increments are considered 0.1, 0.05, and 0.01 tE(0,70) User the FDM central method. RUnge-kutta method and analytical solution and compare your results
Problem #3 a) Determine if the next second order system is oscillating, low damped, critically damped or overdamped. Justify your conclusion. G(s)10 s2 +s +1 b) Determine the maximum percentage overdrive (if any) and the set time to the 2% criterion that will have the response to the unit step of the previous system. c) Plot the response to the magnitude 5 step of the G (s) system.
We are designing a system that is critically damped. Consider a spring mass damper design where mass is m=1 kg and the system has to be critically damped. If we want y(t)=te-t as the response, determine the damping constant b and spring constant k. Since it is critically damped, also find the two initial conditions that gives the desired response.
Need to solve problem with Simulink. Need to identify if over damped, critically damped, or under damped. Need to try 2 other coefficients, with explanations. Need screenshot of positiok graphs for all 3 modes, along with screenshot of simulink solution. Figure 7: Velocity components of projectile at some instant 4.2 Problem #2 The second problem is related to viscous damped free vibration discusion and is problem# 2272 in the textbook. The details of the assignment are given below (You can...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
find general solution y" - 8y' + 17y = 0 is solution undamped, critically damped, over damped, or under damped?
For the system shown below, find the followings; (a) Make an accurate plot of the root locus (b) The value of K that gives a stable system with critically damped second-order poles (c ) The value of K that gives a marginally stable sytems Cs) (s-20s- I) 0.5 The characteristic equation (denominator of the closed-loop trans fer function set equal to zero) is given by For the system shown below, find the followings; (a) Make an accurate plot of the...
Determine the value of the damping coefficient c for which the system is critically damped if k = 50 kN/m and m = 97 kg.
A damped system consists of a mass (m = 30kg) supported on a spring and a damper in parallel. In an experiment, the period of vibration of this system was measured to be 0.5 seconds, and the ratio of maximum displacement between two successive cycles was determined from the experimental data to be 20. Determine: a. The logarithmic decrement. [2] Q4a. Answer: b. The damping ratio, commenting if this is over-damped, critically damped, or under-damped. [4] Q4b. Answer: c. The...