2. (30 pts) Consider the system of Figure 1 (m-2 kg, k 50 N/m, 0-30°). a) Obtain the equation of motion. b) Compute the initial conditions such that the system oscillates at only one frequency wh...
2. (30 pts) Consider the system of Figure 1 (m-2 kg, k 50 N/m, 0-30°). a) Obtain the equation of motion. b) Compute the initial conditions such that the system oscillates at only one frequency when Fa)-2sin10 c) Calculate the response of the system for F)-2sin10/, xo-0,-10 m/s. d) Calculate the response of the system for F)-108t), xo-0, -10 m/s. c) Calculate the response of the system for F(i)-2sin10+108(-2), x0-0, ao-10 m/s. nt Ft) Figure 1. Mass-spring system
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.
1. Consider a spring-mass-damper system with equation of motion given by: 2! x!+8x! + 26x = 0 . i) Compute the solution if the system is given initial conditions x0 = 0 and v0 = -3 m/s j) Compute the solution if the system is given initial conditions x0 =1 m and v0 = −2 m/s k) Compute the solution if the system is given initial conditions x0 = −1 m and v0 = 2 m/s 2. Compute the solution...
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...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
Design dala Observalion deck mass m-25,000 k Danong ratio 0.5% Figure 91. Determine the equation of motion ofthe ๒wer teevibraorntheform (15 marks) mitt) + car)+xt)- where xt) is the horizontal displacement of the top of the tower b) Determine the damped natural frequency, fa (in Hz) of the tower (10 marks) ) A radar device, which inckdes a large rotaling eccentic mass, has been (30 marks) nstalled at the top of the tower Unfortunately, it has a trequency of rotation...
4. (35 pts) Consider the system defined by: xit 5x1-2x2-R (1) #2-2x, +2x2 F) a) Compute the natural frequencies and the mode shapes. /dland -JS -2N5 b) Calculate the response for F(t)-F(t)-0 and initial conditions xo- e) Calculate the response for F-cosr, F,(o)-0 and initial conditions and -0. 0 d) Calculate Bi and B2 such that the system: -2x1 + 2x2-B2cos/6t does not experience resonance. 4. (35 pts) Consider the system defined by: xit 5x1-2x2-R (1) #2-2x, +2x2 F) a)...
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
Problem 1: For the system in figure (1-a), the spring attachment point B is given a horizontal motion Xp-b cos cut from the equilibrium position. The two springs have the same stiffness k 10 N/m and the damper has a damping coefficient c. Neglect the friction and mass associated with the pulleys. a) Determine the critical driving frequency for which the oscillations of the mass m tend to become excessively large. b) For a critically damped system, determine damping coefficient...
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m, b= 3 m, k = 2500 N/m, c= 30 N.s/m, is subjected to a force excitation F(t)= F, sin(ot), where F = 1000 N. Find the maximum steady-state displacement of the mass for each of the following case: 1. The excitation frequency, o, is in the rage of 0-3 Hz. 2. The excitation frequency, o, is in the rage of 3-10 Hz 3. The...