A two-degree-of-freedom system has: (a) one mode shape (c) two mode shapes (b) four mode shapes...
1. Consider the two degree of freedom system shown. (a) Find the natural frequencies for the system (b) Determine the modal fraction for each mode. (c) Draw the mode shapes for each mode and identify any nodes for each mode. (d) Demonstrate mode shape orthogonality. (e) If F- and the motion is initiated by giving the mass whose displacement is a velocity of 0.2 m/s when in equilibrium, determine 0) and ,0 (f) Determine the steady-state solution for both *)...
If the first and second mode shapes, normalised with respect to the mass matrix, of an undamped two degree of freedom system are given by: -0.009) (-O 015 01 = {0.0143; 02 = 0.012) and the stiffness matrix is: K = _4 24]* 106 N/m then, calculate the natural frequencies. (30%)
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2 For the system shown in Figure...
13. Briefly describe how a two degree of freedom system can be made to vibrate in one of its pure modes. sャ 2. (a) Sketch the amplitude ratio and phase angle for damping of 0.01 and 0.3, and indicate the peak amplitude values. Name the axes with correct numerica (b) Compare this amplitude diagram with a similar one that corresponds to base excitation, emphasizing t a single degree of freedom system subjected to harmonic force with phasizing the differences (15)...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end is fixed and K1 and K2=K (5) Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes Determine and explain how to get the natural frequencies 1. (5) (5) 2. 3. Figure 5 ww ww- For the system shown in Figure 5, a. How many degrees of freedom...
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...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www Problem 5 (20%) For the system shown in Figure...
2) A single degree of freedom system is excited by sinusoidal force. Determine the damping ratio of the system if the amplitude of displacement at resonance is 2 in, the exciting frequency is one- tenth of the natural frequency and the amplitude of displacement at resonance is 0.2 in a) 0.25 Hz b) 0.5 Hz c) 0.0025 Hz d) 005 Hz 2) A single degree of freedom system is excited by sinusoidal force. Determine the damping ratio of the system...
3. Consider a two-factor factorial design with three levels in factor A, four levels in factor B, and four replicates in each of the 12 cells. Complete parts (a) through (d). a. How many degrees of freedom are there in determining the factor A variation and the factor B variation? There is/are degree(s) of freedom in determining the factor A variation. (Simplify your answer.) There is/are degree(s) of freedom in determining the factor B variation. (Simplify your answer.) b. How...
subject of mechanical vibrations Q2) Mark a circle on the correct answer: 1) Lagrange equation can be applied: A-only for single degree of freedom system. C-only for multiple degree of freedom system. 2) coordinate couplings is considered as: A-single degree of freedom. C-third degree of freedom. B- only for two degree of freedom system. D- for any dynamical system. B-second degree of freedom. D-fourth degree of freedom. 3) Dynamic absorber for undamped system is composed of: A-spring only to be...