Homework Answers
4. Three forces of 2 N, 3 N and 4N act as shown below: Calculate the...
4. Three forces of 2 N, 3 N and 4N act as shown below: Calculate the magnitude of the resultant and it's direction relative to the 2 N force. [6.24 N at 76.10°] 4N 60 3N 60° 2 N 1.5 m/s2 at 90° and b 2.6 m/s2 at 145° act at a [2.13 m/s2 at 0°] 5. Acceleration of a point. Draw a diagram and find a - b
Q2. Derive the governing differential equations for the systems shown in the following figures. fv=4 N-s/m K=5 N/mfv =...
Q2. Derive the governing differential equations for the systems shown in the following figures. fv=4 N-s/m K=5 N/mfv = 4N-s/m 000 M1 4 kg f)_ M2 4 kg fv2 4 N-s/m fv= 4 N-s/m (a) fit) Frictionless N/m -xj(t) O000 16 N-s/m 15 N/m 0000 4 N-s/m M1 8 kg M2-3 kg Frictionless Frictionless (b)
Q2. Derive the governing differential equations for the systems shown in the following figures. fv=4 N-s/m K=5 N/mfv = 4N-s/m 000 M1 4 kg f)_...
(20pts) Consider the vertical spring-mass-damper system shown below, where m 2 kg, b 4 N-s/m, and...
(20pts) Consider the vertical spring-mass-damper system shown below, where m 2 kg, b 4 N-s/m, and k 20N/m. Assume that x(0) 0.1 m and (0) 0. The displacement is measured form the equilibrium position. Derive a mathematical model of the system (i.e. an ODE). Then find x(t) as a function of time t.
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3...
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3 8N/m. u(t)2 1(t) is the input of the system and the displacement of the mass, z1(t) is the output. a. b. c. Find the governing equations of the system Find the state space model (matrices, A, B. C, D) Will you see any oscillation in the trajectory of the displacement a? Explain while using the eigenvalues of the system matrix. Hint. Eigen values of...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s...
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...
2. For the following system, assume that m-2 kg, b-3 N-s/m. and k-100 N/m. The mass...
2. For the following system, assume that m-2 kg, b-3 N-s/m. and k-100 N/m. The mass is displaced for 0.04 m and it is released without initial velocity. If the displacement is measured from the equilibrium position, find the frequency observed in the vibration. Also, find the amplitude when t-4/oa IN
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using...
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the following data: m 10 kg. k 1000 N/m, integral, (b) sketch the response. F(t) 50 (1
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the...
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using...
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the following data: m 10 kg. k 1000 N/m, integral, (b) sketch the response. F(t) 50 (1
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the...
1. Consider the system shown. Assume B-3 N-s/m and K-7 N/m. Negligible Mass a) Find the...
1. Consider the system shown. Assume B-3 N-s/m and K-7 N/m. Negligible Mass a) Find the transfer function, H(s)-X(s)Fa(s) b) Using the transfer function, find the unit step response and the unit impulse response. c) Using the transfer function, find the steady-state response when fa(t) 2 sin (4t) d) Find the free response (zero-input response) assuming x(0) 2 m.
A 2 kg solid cylinder can rotate about its central axis through point applied as shown: F1 = 6 N, F2 = 4N, F3 = 10 N and F4 = 20 N.
A 2 kg solid cylinder can rotate about its central axis through point applied as shown: F1 = 6 N, F2 = 4N, F3 = 10 N and F4 = 20 N. The positio torces are applied are R = 6 cm and R2 = 12 cm. During the rotation, all forces same angles relative to the cylinder. Find the angular acceleration (magnitude and direction) of the cylinder.
4. Three forces of 2 N, 3 N and 4N act as shown below: Calculate the magnitude of the resultant and it's direction relative to the 2 N force. [6.24 N at 76.10°] 4N 60 3N 60° 2 N 1.5 m/s2 at 90° and b 2.6 m/s2 at 145° act at a [2.13 m/s2 at 0°] 5. Acceleration of a point. Draw a diagram and find a - b
Q2. Derive the governing differential equations for the systems shown in the following figures. fv=4 N-s/m K=5 N/mfv = 4N-s/m 000 M1 4 kg f)_ M2 4 kg fv2 4 N-s/m fv= 4 N-s/m (a) fit) Frictionless N/m -xj(t) O000 16 N-s/m 15 N/m 0000 4 N-s/m M1 8 kg M2-3 kg Frictionless Frictionless (b)
Q2. Derive the governing differential equations for the systems shown in the following figures. fv=4 N-s/m K=5 N/mfv = 4N-s/m 000 M1 4 kg f)_...
(20pts) Consider the vertical spring-mass-damper system shown below, where m 2 kg, b 4 N-s/m, and k 20N/m. Assume that x(0) 0.1 m and (0) 0. The displacement is measured form the equilibrium position. Derive a mathematical model of the system (i.e. an ODE). Then find x(t) as a function of time t.
Problem 1: For the mechanical system shown below, m-2 kg, b-2 N/(m/s). ki 10N/m, k2-2N/m, k3 8N/m. u(t)2 1(t) is the input of the system and the displacement of the mass, z1(t) is the output. a. b. c. Find the governing equations of the system Find the state space model (matrices, A, B. C, D) Will you see any oscillation in the trajectory of the displacement a? Explain while using the eigenvalues of the system matrix. Hint. Eigen values of...
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...
2. For the following system, assume that m-2 kg, b-3 N-s/m. and k-100 N/m. The mass is displaced for 0.04 m and it is released without initial velocity. If the displacement is measured from the equilibrium position, find the frequency observed in the vibration. Also, find the amplitude when t-4/oa IN
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the following data: m 10 kg. k 1000 N/m, integral, (b) sketch the response. F(t) 50 (1
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the...
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the following data: m 10 kg. k 1000 N/m, integral, (b) sketch the response. F(t) 50 (1
Tutorial 9 Transient Vibration as shown below. (a) Find the response of 40 N s/m; using 1he convolution Q.1 An nderdamped system is subjected to a transient force the system given the...
1. Consider the system shown. Assume B-3 N-s/m and K-7 N/m. Negligible Mass a) Find the transfer function, H(s)-X(s)Fa(s) b) Using the transfer function, find the unit step response and the unit impulse response. c) Using the transfer function, find the steady-state response when fa(t) 2 sin (4t) d) Find the free response (zero-input response) assuming x(0) 2 m.
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