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Problem 3.(30 pts) Derive the equation of motion and find the steady state response of the...
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P...
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
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...
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1....
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1. The hinges are free to rotate. 0 denotes the rotational angle of the rod, and 0-0 when all springs are not stretched. The mass of the bar and the size of the mass are negligible. Neglect gravitational force, and assume 0 is very small. 1) Derive the equation of motion for this system with Lagrange's method. (20pt) 2) Find the natural frequency of the...
Use only newtons method and make free body diagram Derive the equation of motion and find...
Use only newtons method and make free body
diagram
Derive the equation of motion and find the natural frequency of the system shown below. Given that the moment of inertial of the bar about its centre of gravity is Jg = 1 ml? 4 Uniform rigid bar, mass m 3K @ooo k 4 4 2 Hint: the moment of inertia of the bar about O is to be found first.
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
Please show what basic mechanical equations are used or explain how to derive the equation. Not...
Please show what basic mechanical equations are used or
explain how to derive the equation. Not just looking for the
answer.
c 60 kg/s is subject to a A damped harmonic oscillator with m - 10 kg, k 250 N/m, and driving force given by Fo cos ot, where Fo 48 N. (a) What value of ω results in steady-state oscillations with maximum amplitude? Under th condition:
problems 20,24 plz St rol In crns (section 6.4) 19-25 the steady-state response of the mechanical system shown in Figure P19-p25 is sought. The systenm problems arameter values m-l, b-0...
problems 20,24 plz
St rol In crns (section 6.4) 19-25 the steady-state response of the mechanical system shown in Figure P19-p25 is sought. The systenm problems arameter values m-l, b-0.1, k -20, in consistent units, and is subjected to a periodic applied force f .Note that when this system is subjected to F cos ot, the steady-state response is exactly as in Eq. (3.30) of Section 3,4, with the sine function replaced by the cosine function! 19 )-sin 2 f(t)-2...
Problem 2 (30 pts) team enters a well-insulated turbine operating at steady state with a mass flo...
Problem 2 (30 pts) team enters a well-insulated turbine operating at steady state with a mass flow rate inlet conditions of the steam are 80 bar, 480°C, and 75 m/s, and the exit conditions are quality, and 40 m/s. The elevation of the inlet is 5 m lower than at the exit. (a) (20 points) the power developed by the turbine, in kW (b) (10 points) the turbine inlet area in em2. Here, I m 100 cm of 5760 kghr....
1. Derive equation of motion 2. Use Laplace transformation to get the analytical solution. 3. Fin...
1. Derive equation of motion 2. Use Laplace transformation to get the analytical solution. 3. Find expression of displacement and velocity Problems I. An instrument is attached to a base whose motion is to be measured. The relative motion between mass m and the base recorded by a rotating drum will indicate the motion of the base. Assume that x is the displacement of the mass, y is the displacement of the base, and z x-y is the motion of...
Name PROBLEM 2: (18%) Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response yo) subject to u(t...
Name PROBLEM 2: (18%) Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response yo) subject to u(t) frequency response formula.) (9%) (Easy) 3cos (0.5t-0.5). (Hint: use the
Name PROBLEM 2: (18%) Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response yo) subject to u(t) frequency response formula.) (9%)...
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
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...
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1. The hinges are free to rotate. 0 denotes the rotational angle of the rod, and 0-0 when all springs are not stretched. The mass of the bar and the size of the mass are negligible. Neglect gravitational force, and assume 0 is very small. 1) Derive the equation of motion for this system with Lagrange's method. (20pt) 2) Find the natural frequency of the...
Use only newtons method and make free body
diagram
Derive the equation of motion and find the natural frequency of the system shown below. Given that the moment of inertial of the bar about its centre of gravity is Jg = 1 ml? 4 Uniform rigid bar, mass m 3K @ooo k 4 4 2 Hint: the moment of inertia of the bar about O is to be found first.
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
Please show what basic mechanical equations are used or
explain how to derive the equation. Not just looking for the
answer.
c 60 kg/s is subject to a A damped harmonic oscillator with m - 10 kg, k 250 N/m, and driving force given by Fo cos ot, where Fo 48 N. (a) What value of ω results in steady-state oscillations with maximum amplitude? Under th condition:
problems 20,24 plz
St rol In crns (section 6.4) 19-25 the steady-state response of the mechanical system shown in Figure P19-p25 is sought. The systenm problems arameter values m-l, b-0.1, k -20, in consistent units, and is subjected to a periodic applied force f .Note that when this system is subjected to F cos ot, the steady-state response is exactly as in Eq. (3.30) of Section 3,4, with the sine function replaced by the cosine function! 19 )-sin 2 f(t)-2...
Problem 2 (30 pts) team enters a well-insulated turbine operating at steady state with a mass flow rate inlet conditions of the steam are 80 bar, 480°C, and 75 m/s, and the exit conditions are quality, and 40 m/s. The elevation of the inlet is 5 m lower than at the exit. (a) (20 points) the power developed by the turbine, in kW (b) (10 points) the turbine inlet area in em2. Here, I m 100 cm of 5760 kghr....
1. Derive equation of motion 2. Use Laplace transformation to get the analytical solution. 3. Find expression of displacement and velocity Problems I. An instrument is attached to a base whose motion is to be measured. The relative motion between mass m and the base recorded by a rotating drum will indicate the motion of the base. Assume that x is the displacement of the mass, y is the displacement of the base, and z x-y is the motion of...
Name PROBLEM 2: (18%) Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response yo) subject to u(t) frequency response formula.) (9%) (Easy) 3cos (0.5t-0.5). (Hint: use the
Name PROBLEM 2: (18%) Given the following differential equation (a) Find the forced response y(t) to a unit ramp input of u(t). (9%) (Medium) (b) Find the steady-state response yo) subject to u(t) frequency response formula.) (9%)...
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