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- A certain mass is driven by base excitation through a spring (Figure P4.13). Its parameter values are m = 100 kg, c = 1000 N * s/m, and k = 10,000 N/m. Determine its peak frequency w_p, it’s peak M_p, and its bandwidth.Sketch the level response for a bathtub with cross-sectional area of 8 ft 2 as a function of time for the following sequence of events; assume an initial level of 0.5 ft with the drain open. The inflow and outflow are initially equal to2ft3/min.(a)The drain is suddenly closed, and the inflow remains con-stant for 3 min (0≤t≤3).(b)The drain is opened for 15 min; assume a time constant in a linear transfer function of 3 min, so a steady state is essentially reached (3≤t≤18) (c)The inflow rate is doubled for 6 min (18≤t≤24).(d)The inflow rate is returned to its original value for 16 min(24≤t≤40).Obtain the following requirements for a simple mass-spring-damper system with input of force f, output of displacement x, and translational motion only along the horizontal axis.a) Equation of motion,b) state space model,c) transfer function G(s),d) the time domain expression of the output according to the unit step function input,e) permanent regime error to be observed at the output according to the unit step function input,f) pole and zero positions in the complex plane,g) its absolute stability,h) the undamped natural frequency,i) damping ratio,j) damped natural frequency,k) open loop/static/dc gain,l) maximum overshoot (Mp),m) peak time (tp),n) settling time (ts, 2% tolerance).
- A system has the following characteristic equation: s+ s+ 3s+ 2s + 2 = 0 Using the Routh-Hurwitz method, checka. How many roots are to the right of the imaginary axis?b. Is the system stable?.A vibrating spring-mass system has the feedback control system shown in Fig Q3 below. (figure attached as image ACT)If K = 12.25 determine:6.1 the transfer function ; (3)6.2 the characteristic equation with a impulse input; (1)6.3 the un-damped natural frequency of the system; (2)6.4 the damping ratio; (2)6.5 the damped natural frequency; (2)6.6 the maximum percentage overshoot; (2)6.7 the peak time; (1)6.8 the settling time for the response within 2%. (2)The block diagram given below; A) Reduce it B) G1(s)=2/s ; G2(s)=1/4s+2 ; G3(s)=4 ;H(s)=0.5 Given the values of the system; find the time constant, its natural frequency and damping rate and explain what kind of dynamic behavior it exhibits accordingly. C)Find the poles and zeros of the system according to the values in (B).Is the system stable? Find the unit step response (Inverse Laplace).
- A cantilever beam of length 700 mm, width 55 mm, and thickness 15 mm is made of steel with Young’s modulus 200 GPa and mass density 7800 kg/m3. The displacement model is assumed to be w(x,t)=q1(t)x2L2w ( x, t ) = q 1 x 2 L 2 where L is the beam length. The damping in the beam is negligible. The beam is excited at a location 300 mm from the clamped end with a translational force (in the more flexible direction) of magnitude 10 N at a frequency of 21 Hz (the end of the lecture on adding discrete elements to beam problems gives more detail about including external forces). The maximum steady-state response of the end of the beam (in mm) is The answer has to be one of the options otherwise it will be incorrect. Please don't post if its not one of the options otherwise I will have to downvote. Thanks.A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
- The transfer function of a system is the ratio between _________________ and ____________ in Laplace transform. a. Output and Input b. Input and Output c. Input and Feedback d. Output and FeedbackRepresent the translational mechanical system shown in state space, where x3(t) is the output.Suppose a spring with spring constant 7 N/m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N⋅s/m a) Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x,x′,x′′. Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. b) Find the general solution to your differential equation from the previous part. Use c1 and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Your answer should be an equation of the form x=… c) Enter a value for the damping constant that would make the system critically damped. ?Ns/m