Question 1 (a)
Writing the Torque Balance Equation
Substituting the values
So the differential equation that relates applied Torque and the angular displacement is
Question 1(b)
Taking Laplace Transform on both sides, assuming zero initial conditions
We have used the differentiation property of Laplace transform under zero initial conditions which states that
If
Then
So the differential equation in Laplace domain is
Question 1(c)
So the transfer function is
s) Given the following rotational mechanical system, hot relates the input variable T (applied torque) to...
Q2 A rotational mechanical system is shown in Figure 2.1. T(t) is the external torque and is the input to the system. 01(t) is the angular displacement of inertia Ji and O2(t) is the angular displacement of inertia J2. C and C are friction coefficients and K, and K2 are spring constants. (a) Draw the free-body diagrams for J; and Jz. (7 marks) (b) Derive the equations of motion for the system shown in Figure 2.1. (8 marks) (c) Using...
Question 3) Consider the mechanical system shown in figure, T(t) is the torque applied to shaft 1 and z(t) is the rotation of shaft 2. J.Jz and Jz are the inertias of shafts 1,2 and 3 respectively, N,,N,N, and N, are the number of teeths of the gears,, D1, D, and D3 are the coefficient of viscous damping associated with shafts 1, 2 and 3 respectively, K is the spring constant of the torsional spring attached to shaft 3. Write...
Consider the rotational system with angular velocity "Ω(t)" and input torque "T(t)." TC From Newton's Law, the equation of motion is J Ω(t)-B. Ω(t) Now suppose that this input torque is supplied by an electric motor Specifically, T(t) T(t) -Kamp Vin(t) where 1) "Vin is the input voltage supplied to the motor N-m 2) "Kamp" is the motor gain (this constant has units of Volt) So, the transfer function for this system is (s)Kamp The moment of inertia is known...
θ2(s)/T(s) for the following rotational mechanical system Problem 4: Find the transfer function G(s) TO) N1 = 4 Di 1 N-m-s/rad N2 121 kg-m2 N3-4 D2-2 N-m-s/rad K 64 N-m/rad- N4 16 D3 32 N-m-s/rad -16 kg-m2 000
The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut + ?) N. The differential equation of the displacement x(t) is Use phasor techniques to solve for the displacement phasor Xin terms of the excitation frequency ? , and the mechanical elements M = 0.1 kg, D = 8 N-s/m , and K = 2,000 N/m . If Fi-10 N and ?? = 30°, determine the excitation frequency w (in rad/s) at which the...
PARTS: a-c Problem 1 (40 points) The rotational system shown in this diagram has a single torque input, T(t), and a single angular displacement output, (t). Also shown are the shaft polar moment of inertia, J, torsional spring constant, k, and rotational viscous damping coefficient, c. From the law of rotation (sum of the moments equal to polar moment of inertia times angular acceleration), we obtain: jä(t) + c)(t) + ko(t) = T(t). This ordinary differential equation is second-order, linear...
3.2 Pre-Lab Assignment When deriving the governing equations for an electromechanical system, it is often beneficial to examine the electrical and mechanical components independently. Looking at only the electrical components of the QUBE-Servo DC motor (as shown in Figure 3.2): R v00 C e, (00 Figure 3.2: Electrical curcuit of the QUBE-Servo DC motor Q1. Write the differential equation in the form of Kirchoff's voltage law) in the Laplace domain for the electrical circuit (do not use parameter values given...
Question 3 Find the transfer function, G(s) s) / T(s), for the rotational mechanical system in Fig. Q3 below. The gears have inertia and bearing friction as shown. (20 marks) 3 Nm/rad 2 Nms/rad + 1 kg/m? N3 = 100 N2 = 100 T(t) N4 = 20 N = 20 0.04 Nms/rad Fig. Q3
Q5 The equation of the motion of the mechanical system shown in the following figure is governed by the following differential equation d2 x dx m7+9+= -f(t) - 3kx dt2 dt where m, C and k are mass, damping coefficient and spring constant, respectively. Consider the system with m = 10 kg, c = 80 Ns/m, k = 50 N/m, and the system is at rest at time t = 0 s. f(t) is the external force acting on the...
please show steps For the system shown in the figure. a. Find the transfer function 0,(s)/T(S). b. Find the damping Dyo yield a 20% gvershoot in output angular displacement for a step torque input. N =25 kg-r W3 10 N2=5 D N-m/rad N4 5 0000 For the system shown in the figure. a. Find the transfer function 0,(s)/T(S). b. Find the damping Dyo yield a 20% gvershoot in output angular displacement for a step torque input. N =25 kg-r W3...