Question 5: Determine the natural frequencies and mode shapes of the system 192 shown in Fig. write the equation of motion in the general form of; = C₁₁ sin(w₁t + 1) + C22 sin(w2t + 2) where P₁ = {11} and 42 = (A21 (A22) 3k wwww wwwww k mwww ** 2m www TAZ

Q5. For a point at distance 50 m and angle 450 to the axis which of the following statements are correct? Consider an infinite baffled piston of radius 5 cm driven at 2 kHz in air with velocity 10 m/s. You may choose multiple options. a. The constant term is given by 515.03 b. The distance dependent term is given by e-jk50/50 c. The directivity term is given by j1(Ka sin 450)/sin 450 d. There is no time dependent term.

The parameters of the system are given as: m=1kg ; l=2m ; k=1000N/m ; M0=10Nm   i) Make a modal analysis and calculate natural frequency and those modes shapes ?

Solve the inverse kinematic problem for the following 6 DOF robot, using the method ofkinematic decouplingif it is known that its Denavit-Hartenberg parameters are as shown in the table inthe table

H-W Find Time response for 2S+3 Yes)= s° (s+3)

Problem 3) The Equations of Motion for a system are given as: [2k -k][X1 + -k 3k. [m1 Where m, =m, m2 =2m a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine \x2(t)S d) If an excitation force F1(t) = Fo Cosot acted upon the mass m1, Determine the system response.

2. The equation of motion for a damped multidegree of freedom system is given by Where [m] = [m]{x} + [c]{x} + [k]{x} = {f} [100 = 0 0 0 10 0 10. 1000-4 {f} [c] 8 –4 0 8 – 4 -4 4 0 8 4 = 100 2 0 = Focos(wt) -2 -2 The value of Fo 50N and w 50 rad/sec. Assuming the initial conditions to be zero and using the modal coordinate approach, find out the steady state solution of the system in the modal coordinate for first mode. Plot the steady state solution using the computational tools. 0 −2], [k] = = 2

Please answer: How many degrees of freedom are in the system Write out the equations of morion in matrix form  & Find the natural frequencies Given:  k = 10 N/m; r = 0.5 m; I1 = 1.25 kg*m2 ; I2 = 1.2 kg*m2; m = 1 kg

As a phase line, use a U-shaped curve. Let its downward-sloping segment intersect the 45 degree line at point L, and let its upward-sloping segment intersect the 45° line at point R. Answer the following five questions: (a) Is this a case of multiple equilibria? (b) If the initial value y0 lies to the left of L, what kind of time path will be obtained? (c) What if the initial value lies between Land R? (d) What if the initial value lies to the right of R? (e) What can you conclude about the dynamic stability of equilibrium at L and at R, respectively?

Magnitude (dB) Phase (deg) The system Bode plots are: -50 -100 -90 -135 -180 -225 -270 10¹ 10⁰ Bode Diagram Frequency (rad/sec) a) The system is stable. b) The system is unstable. c) The system is marginally (critically) stable.