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PROF. #1:25%) X(t) = x, sincept) DISPLACEMENT merized o LA LA 2/2 THE SYSTEM تم بحاج...
Problem #2 The displacement x(t) of a cart that is a part of the mass-spring system...
Problem #2 The displacement x(t) of a cart that is a part of the mass-spring system is described by the differential equation dx dx + 2x 0 +3 dt with the following initial conditions: x (0)1 where to is the unknown POSITIVE initial velocity of the cart. The volue of must be found from th condition that the maximum of the dixplecement x(e)for ositive tvoles is equel to 2 (0)o Calculate the required value of , round it off to...
Problem #2 The displacement x(t) of a cart that is a part of the mass-spring system...
Problem #2 The displacement x(t) of a cart that is a part of the mass-spring system is described by the differential equation dax dx dt2 +3 + 2 x=0 with the following initial conditions: H *(0) = 1, (O) = vo, where v, is an unknown POSITIVE initial velocity of the cart. The value of v, must be found from the condition that the maximum of the displacement *(t) for positive t-values is equal to Calculate the required value of...
-2 points SerCP111 3 OP02 Notes O As (a) Suppose that the displacement x of an...
-2 points SerCP111 3 OP02 Notes O As (a) Suppose that the displacement x of an object is related to time t according to the expression x-Br2 What are the dimensions of 87 O LT O LIT2 (b) Suppose the displacement x of another object is related to time t according to x -A sin(2ft), where A and fare constants. What are the dimensions of A? (Hint: A trigonometric function appearing in an equation must be dinensionless.) T/L
Figure 1 shows a slender beam pivoted at point O. Its mass moment of inertia, taken...
Figure 1 shows a slender beam pivoted at point O. Its mass moment of inertia, taken about an axis that goes through point o, is J The rotational motion of the beam about point O can be described by angular displacement θ Formulate the equation of motion of this system using Lagrange's method. Express this equation in terms of Jo. c c. k and / (a) [10 marks] (b) Detemine the values of the system's undamped natural frequency, damping ratio...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
In case of Wiens' Displacement law, the Amax T value equals to O.0.2898 x 10-2 m-K...
In case of Wiens' Displacement law, the Amax T value equals to O.0.2898 x 10-2 m-K Ob.2898 x 10-2 m-K OC. 2.898 x 10-2 m-K d. None
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m,...
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m, b= 3 m, k = 2500 N/m, c= 30 N.s/m, is subjected to a force excitation F(t)= F, sin(ot), where F = 1000 N. Find the maximum steady-state displacement of the mass for each of the following case: 1. The excitation frequency, o, is in the rage of 0-3 Hz. 2. The excitation frequency, o, is in the rage of 3-10 Hz 3. The...
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a...
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a vertical plane under the influence of gravity can be modelled with the second order non-homogeneous ODE 0"(t) + 270'(t) +w20(t) = f(t), (2) where wa = g/l. The second term in the equation represents the damping force (e.g. air resistance) for the given constant 7 > 0. The model can be used to approximate the motion of a magnetic pendulum bob being driven by...
solve the following question For the system shown in the figure below x and y denote,...
solve the following question
For the system shown in the figure below x and y denote, respectively, the absolute displacements of the mass m and the end Q of the damper c1 (1) Derive the equation of motion of the mass m (2) Find the steady state displacement of the mass m (3) Find the force transmitted to the support at P when the end Q is subjected to harmonic motion y (t)-y cos wt x(t) y(t) cos ω t
2. (25%) Consider an undamped system subject to a rectangular pulse given by F(t) Fo for...
2. (25%) Consider an undamped system subject to a rectangular pulse given by F(t) Fo for 0sts to and Ft) = 0 for t > to (a) Find the displacement response x() for 0ststo and t>to, respectively. (b) Find xmax for 0ststo and t> to, respectively.
2. (25%) Consider an undamped system subject to a rectangular pulse given by F(t) Fo for 0sts to and Ft) = 0 for t > to (a) Find the displacement response x() for 0ststo...
Problem #2 The displacement x(t) of a cart that is a part of the mass-spring system is described by the differential equation dx dx + 2x 0 +3 dt with the following initial conditions: x (0)1 where to is the unknown POSITIVE initial velocity of the cart. The volue of must be found from th condition that the maximum of the dixplecement x(e)for ositive tvoles is equel to 2 (0)o Calculate the required value of , round it off to...
Problem #2 The displacement x(t) of a cart that is a part of the mass-spring system is described by the differential equation dax dx dt2 +3 + 2 x=0 with the following initial conditions: H *(0) = 1, (O) = vo, where v, is an unknown POSITIVE initial velocity of the cart. The value of v, must be found from the condition that the maximum of the displacement *(t) for positive t-values is equal to Calculate the required value of...
-2 points SerCP111 3 OP02 Notes O As (a) Suppose that the displacement x of an object is related to time t according to the expression x-Br2 What are the dimensions of 87 O LT O LIT2 (b) Suppose the displacement x of another object is related to time t according to x -A sin(2ft), where A and fare constants. What are the dimensions of A? (Hint: A trigonometric function appearing in an equation must be dinensionless.) T/L
Figure 1 shows a slender beam pivoted at point O. Its mass moment of inertia, taken about an axis that goes through point o, is J The rotational motion of the beam about point O can be described by angular displacement θ Formulate the equation of motion of this system using Lagrange's method. Express this equation in terms of Jo. c c. k and / (a) [10 marks] (b) Detemine the values of the system's undamped natural frequency, damping ratio...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
In case of Wiens' Displacement law, the Amax T value equals to O.0.2898 x 10-2 m-K Ob.2898 x 10-2 m-K OC. 2.898 x 10-2 m-K d. None
Question # 1: [25%] The system in the figure, m= 4 kg, a = 2 m, b= 3 m, k = 2500 N/m, c= 30 N.s/m, is subjected to a force excitation F(t)= F, sin(ot), where F = 1000 N. Find the maximum steady-state displacement of the mass for each of the following case: 1. The excitation frequency, o, is in the rage of 0-3 Hz. 2. The excitation frequency, o, is in the rage of 3-10 Hz 3. The...
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a vertical plane under the influence of gravity can be modelled with the second order non-homogeneous ODE 0"(t) + 270'(t) +w20(t) = f(t), (2) where wa = g/l. The second term in the equation represents the damping force (e.g. air resistance) for the given constant 7 > 0. The model can be used to approximate the motion of a magnetic pendulum bob being driven by...
solve the following question
For the system shown in the figure below x and y denote, respectively, the absolute displacements of the mass m and the end Q of the damper c1 (1) Derive the equation of motion of the mass m (2) Find the steady state displacement of the mass m (3) Find the force transmitted to the support at P when the end Q is subjected to harmonic motion y (t)-y cos wt x(t) y(t) cos ω t
2. (25%) Consider an undamped system subject to a rectangular pulse given by F(t) Fo for 0sts to and Ft) = 0 for t > to (a) Find the displacement response x() for 0ststo and t>to, respectively. (b) Find xmax for 0ststo and t> to, respectively.
2. (25%) Consider an undamped system subject to a rectangular pulse given by F(t) Fo for 0sts to and Ft) = 0 for t > to (a) Find the displacement response x() for 0ststo...
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