Consider the multi-degree of freedom system shown in Fig 1. Let the first four spring constants...
(10 pts) Consider the multi degree of freedom system of Fig. I a) Write the equations of motion. b) Identify the mass matrix and the stiffness matrix Fig. 1 A multi degree of freedom system
Figure Q4 shows a complex multi-degree of freedom spring-mass system. a) Develop the equation of motion of the system. (6 Marks) b) If m - m - m - m and k, = kx - kyky+ ks = k, Determine the natural frequencies and mode shape of the system. (16 Marks) c) Estimate the largest strain that can occur to any of the spring in the system. State which spring in your answer. Marks) (8 ka ka ks ma m2...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
3) For the single degree of freedom system shown below: a) Use the equivalent system method to derive the differential equation governing the motion of the system, taking χ as the Slender har of mass m generalized coordinate. Rigid 1 link b) If m-6 kg, M = 10 kg, and k=500 N/m, determine the value of c that makes the system critically damped. c) For the values obtained in part (b), determine the response of the system, x(t) if x(0)=...
3. Consider the spring - mass system shown below, consisting of two masses mi and ma sus- pended from springs with spring constants ki and k, respectively. Assume that there is no damping in the system. a) Show that the displacements z1 and 2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above resuit to show that the spring-mass system satisfies the following fourth order differential equation. and ) Find the general solution...
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1
Consider a mass-spring system shown below with a hard spring. That is, it requires more force to deform the same amount as the spring stretches/compresses. elle m The equation of motion is given by mä+kx3 = mg, where x is the stretch of the spring from its undeformed length, m is the mass of the block, k is the spring constant, and g is the gravitational acceleration. After the equation of motion is linearized about its equilibrium position, it can...
MatLab work preferred, but please show/describe process. I) 3-DOF Pendulum System Using matrix algebra, analyze the vibration of following 3-DOF pendulum system. Where, a is the distance from the pivot point to the spring, and L is the length of the pendulum string. Derive: the equations of motion, the system natural frequencies and system's mode shapes 01 02 K2 mi m2 m3 Data: mi 5 kg m2 = 5 kg m3 5 kg k1 100 N/m k2 100 N/m L...
44. The system shown in Fig. P7 consists of a slider block of mass m2 and a uniform slender rod of mass m3, length 13, and mass moment of inertia about its center of mass J The slider block is connected to the ground by a spring that has a stiffness coefficient k. The slider block is subjected to the force F(t), while the rod is subjected to the moment M. Obtain the differential equations of motion of this two-degree-of-freedom...