3. (15 points) Find the equations of motion for mi and m2 as shown in Figure 1.jo) is the input force of the system and xi is the output function of the system. Assume gravity is not a factor. of...
For the system in the figure betow, find the differential equations that relate between the input -force Kt) and mass 1, and mass2 velocity? lidu VI f(t) ml m2 mi
Problem # 2 (50pts) m2 Find the equations of motion to describe the system below. The spring produces zero force at zero length. The spring has zero mass, the rod has zero mass. Note: To describe the dynamics, you need 2 Generalized coordinates: 0,x. u g a) Find the velocities of the important components, mi, m2, (10 points). mi b) Find the kinetic energy of the system (10 points). c) Find the potential energy of the system (10 points). d)...
Problem 2) For a 2 DOF system the equations of motion are given as: [mi 0 0 m2 (X2 mig L -m29 L -m29 L m29 L Where m1 =m2 =m g=gravity and L =length a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine the response fX:(0) Note: x1(t) = xo , x2(t) = 0 and xi(t) = xo , iz(t) = 0 d) If the system is excited by a harmonic...
Q2. A mechanical system is shown as Figure 2, where external force uz is the input and displacement y2 is the output. The force acting on m2 has a linear relationship with uj as u2=Aui. 1) List system equations; 2) Draw block diagram of the control system; 3) Build the block diagram in Simulink (screenshot and paste your diagram in your submission). ki U1 mi k2 Yi Y bi U2 V m2 y2 Figure 2
Please write down the steps by steps solution, thank you! Question 1 Figure Q1 shows a mechanical system. The system input is T) and output is supposed to be 0. Please find the transfer function from T to θ 3, and discuss the stability of the system if the input is a unit impulse signal. (30 marks) To 01(t) 01t) I kg-m2 N 10 030) N2 100 100 kg-m2 100 N-m/rad 100 N-m-s/rad Figure Q1 Question 1 Figure Q1 shows...
Consider the mechanical system shown in Figure. Displacements Xi and Xo are measured from their respective equilibrium positions. Derive the transfer function of the system wherein Xi is the input and Xo is the output. Then obtain the response Xo (t) ki bi b,* when input Xi (t) is a step displacement of magnitude Xi occurring at t 0. Assume that Xo (0-) 0.
The mechanism shown in figure 1 converts rotary motion to linear motion. Find the analytical equations relating the input angular displacements/velocities/accelerations and the output linear displacements/velocities/accelerations. Then, writing a computer program, simulate the motion of the mechanism with various motor inputs of θ, θ, θ for the following cases: 1- Assume that θ, θ are equal to zero, Plot the linear displacement when θ is changing with 1 degree increments. 2-Assume that θ is zero, θ is a constant that...
02 Obtain the transfer function Y(s)yU(s) of the system shown in Figure. The vertical motion u at point P is the input. This system is a simplified version of an automobile or motorcycle suspension system. (In the figure mi and ki represent the wheel mass and tire stiffness, respectively.) Assume that the displacements x and y are measured from their respective equilibrium positions in the absence of the input u. Use Newton second law to derive the movement equations.
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
the following problem is of a two-mass system. I have 2 questions 1. find the transfer function from input F2 to output x1 2. for the transfer function found, determine the sensitivity to variation in parameter B12 note: i already found the differential eqns of motion for t>0 Problem formulation Two masses are connected as shown in Fig. 1. Input forces Fi(t) and F.(t) act on masses m, and mg, respectively. The outputs are positions xi(t) and x2(t). Initial conditions...