Problem 3. The mass and stiffness of a SDOF system are 2 ks2/in. and 40 k...
63 Figure P6.3 shows a mass-damper system (no stiffness, Problem 2.3). Displacement x is measured from an equilibrium position where the damper is at the "neutral" position. The external force () is a short-duration pulse function: f(!)-5N for 0SS002 s, and f,() = 0 for t > 0.02 s. The system parameters are mass m-0.5kg and viscous friction coefficient b 3 N-s/m and the system is initially at rest. Usc Simulink to determine the system response and plot displacement xit)...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
4. Consider the mechanical system shown below with a spring with stiffness, k (N/m), in parallel with a viscous damper with coefficient, h (Nós/m) and an externally applied force, Fexi(t) (N). u(t) a. Find the equation that relates the applied force, Fext(t) and the displacement, u(t). b. If the spring component has a stiffness of k = 75 N/m, the damper component has coefficient h = 50 N s/m and the externally applied force is a constant 4.5 N applied...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 = 10 N 92 = 8N, and m = 10 kg subjected to the harmonic force f(t) = qı sin(vt) + 92 cos(vt), v = 1 rad/ sec. Assume zero initial conditions (0) = 0 and c(0) = 0. Derive and plot the analytical solution of the displacement of the system. mm m = f(t) WWWWWWWW No friction Problem 2 Problem 3 (30 points): Using...
Problem 3 (10 points). Consider the weakly coupled mechanical system shown in figure 2. Let are: k be the stiffness of the spring and mi-m2- m. Given that the initial conditions 1(0)0 6,(0)-A Oz(0)-0 02(0)0 I. Compute the complete solution of the system linearized around θ1 θ2 0 2. Given the numerical values in the following table, plot θ1(t) and θ2(t) on the same figure for 0 << 100s. Give a physical interpretation of what is happening Parameter Numerical Value...
Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer function of V(s)/R(s) when Gc(s)-1 2) Derive the closed-loop transfer function of E(s)/R(s) when Ge(s)-1 3) Plot the time history of the error e(t) of the closed-loop system when r(t) is a unit step input. 4) Plot the root-loci of the uncompensated system (when Gc(s)-1). Mark the closed-loop complex poles on...
2. For the following system, assume that m-2 kg, b-3 N-s/m. and k-100 N/m. The mass is displaced for 0.04 m and it is released without initial velocity. If the displacement is measured from the equilibrium position, find the frequency observed in the vibration. Also, find the amplitude when t-4/oa IN
Consider the mass-spring system given below. Suppose that the upper weight is pulled down one unit and the lower weight is raised one unit, then both weights are released from rest simultaneously at time t = 0, The governing differential equations of the system are 1. For mi-m2 1, k1-3, k2 2 and k3 6, find the position of the masses at any time t>0 Note that the initial conditions are yi(0) 1, 32(0)1, 1 (0) 0 and 2(0)-0. For...
2. Consider a spring-mass-damper system with oh-20 rad/s and K-1k = 0.010 mN that is initially at rest [y(0) = dydt(0)-0]. This systern is subjected to a step load F-10 N at t-0·Plot displacement y(t) for range 0StS0.8 for 3 different damping ratios(-0.40,1.00, 1.60) on a single graph (see Eq. 3.15). Use a software package to plot (Excel, MathCad, Matlab, etc.)-do not plot by hand. (12 points)