Problem1: Consider the translational system shown in the figure below. Att-0,x (displacement)-y (...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
Problem1 A speaker is modeled with the system model given in the equations below. 2 m (x) + c(x) + kx = Kyi V(t) = L(i) + Ri + Kc(x) Given that the following constants, m- 2E-3 Kg, c 30 N.s/m, k 1.25E+5 N/m, K- Ke 2.5 Vls.m, L-0.02E-3 Henries (H) and R- 2 and the () indicate time derivatives, Find the maximum displacement, Xmax, when the speaker is given an input of V(t)-sin(2ft) when the frequency is varied between...
mmHg 10-26. The displacement y(t) of a spring-mass system shown in Fig. P10.26 is given by 0.25 y(t)+ 10 y()0 (a) Find the transient solution, yrun() (b) Find the steady-state solution of the displacement ys (c) Determine the total displacement y(t) if the initial displacement y(0) 0.2 m and the initial veloc- ity y(0)-0 m/s (d) Sketch the total displacement y(t). k 10 N/m 0.25 kg y0) mmHg 10-26. The displacement y(t) of a spring-mass system shown in Fig. P10.26...
Problem # 1 (b): Obtain a mathematical model of the system shown below. Problem1: Consider the system shown below which is at rest for t<0. Assume the displacement x is the output of the system and is measured from the equilibrium position. Att-0, the cart is given initial conditions x(0)- xo and dx(0ydt v Obtain the output motion x0)Assume that m-10 kg, b-50 N-s/m, b-70 N-sm, -400 N/m, k2- 600 N/m. da diagam c.rditinstoo)20 추dx(Hat20.5m/s inilia) Problem12i Referring to Problem...
solve the following question For the system shown in the figure below x and y denote, respectively, the absolute displacements of the mass m and the end Q of the damper c1 (1) Derive the equation of motion of the mass m (2) Find the steady state displacement of the mass m (3) Find the force transmitted to the support at P when the end Q is subjected to harmonic motion y (t)-y cos wt x(t) y(t) cos ω t
For the lever system shown, the input to the system is the displacement, y, and the angle θ is the output. The position θ 0 corresponds to the equilibrium position when y-0. The lever has an inertia I about the pivot. Assume small displacements. 3. ki Derive the equation of motion Find the transfer function for the system. Discuss whether or not this system has numerator dynamics and what affect this has on the response Use the tf and impulse...
matlab please matlab please (4) Consider the system described by the following difference equation y(n)1.77y(n-1)-0.81y(n 2)a(n)- 0.5(n -1) (a) Assuming a unit-step input, and using a long enough section of the input constant output y(n) is observed for large n, hence plot the output and determine the value of this constant called G so that a Note: G, y(n) for n0o. (b) Determine and plot the transient response given by: n(n) = y(n)- Go (c) Find the energy of the...
1 - Consider the system shown in the figure below, #1 25 Ks a) Determine the value of k that yields a damping ratio ? of 0.6 b) Based on the numerical value found for k in part (a) of the problem, determine (10 points) the open-loop gain and the system's type. Determine the steady-state errors for the system when it is subjected to (6 points) c) 1. a step reference input, r()-A 2. a ramp reference input, r()-t (6...
6.Assuming De) 0 in the plant given in Fig: 3 with Gs. design a PD controller that drives y(1) to asymptotically follow a unit-step input command i(t) with a percent overshoot equal to 10% and e setling time equal to 0.5 se. Identify the pşak time and the damped frequency of the transient response () Carefully sketch the transient response. Assuming Ds)-, find a steady state error due to this disturbance s(s +5) (0 pts) DS) Ris) E(s) Y(s) g....
Consider the mechanical system shown in Figure. Displacements Xi and Xo are measured from their respective equilibrium positions. Derive the transfer function of the system wherein Xi is the input and Xo is the output. Then obtain the response Xo (t) ki bi b,* when input Xi (t) is a step displacement of magnitude Xi occurring at t 0. Assume that Xo (0-) 0.