Q2. For the system where a vertical mass m is connected to the midpoint of the slender bar of mass m and length L throug

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Q2 For The System Where A Vertical Mass M Is Connected To The Midpoint Of The Slender Bar Of Mass M And Length L Throug 1 (561.61 KiB) Viewed 11 times

Q2. For the system where a vertical mass m is connected to the midpoint of the slender bar of mass m and length L through a spring of stiffness k, denote the displacement of the vertical mass by x and the small rotational angle of the slender bar by 0, respectively. The initial conditions are: x(0) = 0, 0(0) = -0.5 rad, x(0)= 2m/s, 0(0)= 0. Given: m = 4 kg, L = 1m, k = 2KN/m and let its mode shapes be denoted by [X1, X2]T= [x, 0]T. Find the correct answer to each of the questions below (do not show calculations). Questions Answer (a) Answer (b) FBD of the system FBD of the mass and that of the bar What free body diagrams (FBD) need to be done when using Newton's 2nd law to derive equations of motion? Natural frequencies of the system are dependent on the location of the springs and the mass It is known from the given initial the bar has an initial conditions that initial displacement and rotation angle the bar has an initial clockwise rotation angle 0.5 rad mode shapes of the system anticlockwise rotation angle 0.5 rad natural frequencies of the system @₁-33.38 rad/s, 002= 73.38 rad/s 2 A change in initial conditions will lead to the change in Natural frequencies of the system are @₁ = 16.69 rad/s, 002 = 36.69 rad/s 1 How many mode shapes does the system have? the length of the bar Mode shapes of the system are not affected by The mode shapes of the system are found to be [X1,1, X2,1] [1, 0.3]¹ [X₁2X22]¹[1, -0.3] be increased the location of the springs [X₁,1, X₂,1]=[1, 0.5] [X12X22] [1, 0.3]¹ not be affected If a vertical harmonic force is acted on the vertical mass, the free vibration amplitudes of the system will If a harmonic torque is acted on the bar, its excitation frequency will not change either natural frequencies or mode shapes of the system change the mode shapes of the system only Answer (c) FBD of the mass and that of the system the mode shapes of the system m has an upward initial velocity of 2m/s system's free vibration response neither (a) nor (b) is correct more than 2 initial conditions neither (a) nor (b) is correct be reduced change the natural frequencies of the system only wwww Slender bar of mass m Correct answer