Q11// a) Find the equation of motion, delta. Ta and O₁ when = 1 b) same system each of the system find k,c equivalent at spring k shown in Figure (11). 444 3k Uniform rigid bar, k mass m 12 4 Figure 11

Determine the manipulator linear and angular velocity for the 3-DOF articulated armusing Jacobian modelling

* Find the equations of motion of the systems if you know: =mở tan6 5 =- In(ø) 16 R= Q = 0

For the mechanism shown below;i) Show variables on the figure,ii) Determine the space scale, ks=?iii) Write vector loop closure equation(s) by using complex numbers,iv) Solve the vector loop equation in order to determine the relative position ofpiston at point D with respect to point B when 2=60o.

1. Find: Vs, wa/c, and wa/A Use relative motion analysis OR Instantaneous center of rotation Given: 0= 58° @=39° BC=3m AB=9m V₁ = 12 m/s your choice mak 437 B

Q3: Draw the free-body diagram and derive the equation of motion (EOM) using: (1) Newton's 2nd law (2) Energy method for the systems. (3) Find the natural frequency. m 4r 1447 x(t) k 00000 -Pulley, mass moment of inertia Jo

system with m=20, c = 17 Suppose that the mass in a mass-spring-dashpot and k = 3 is set in motion with x(0) = 0 and x'(0) = 8. (a) Find the position function x(t) and show that its graph looks as indicated in the figure. (b) Find how far the mass moves to the right before starting back toward the origin. 3 5 160 (a) x(t) = 7 (Type an exact answer.) 160 7 300 (b) The mass moves 7.1344 units to the right before turning back. (Round to four decimal places as needed.) 0 10 20 30 40 50

Suppose that the mass in a mass-spring-dashpot system with m=20, c = 19 and k = 3 is set in motion with x(0) = 0 and x'(0) = 7. (a) Find the position function x(t) and show that its graph looks as indicated in the figure. (b) Find how far the mass moves to the right before starting back toward the origin. 10 20 30 40 50 Q N

PROBLEM1: Determine the equation of motion of the following systems: 1080 al*k www 0.51 ghiv Vin & Masa Less, Rigid L J Figure 2-Problem 1-2 a3*m

6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support