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The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut...
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force...
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force that is a function of its extension. A damper exerts a force that is a function of the velocity of the piston. Assume that the spring and the damper are both linear. (1) We want to describe the relation between the external force F(t) and the position yt) of the mass. Give the differential equation relating F(t) and y(t). Define this carefully as a...
The function x(t)=cos(2, where f is the sinusoidal frequency, sampled by replacing t with nT, where...
The function x(t)=cos(2, where f is the sinusoidal frequency, sampled by replacing t with nT, where T is the sampling period and n is an integer. The results is the sequence x[n]=cos(2If f=1 MHz=1,000,000, and T is 0.1 microseconds. Write expression for x[n]. Plot x[n] over -8 < n < 8
Q5 The equation of the motion of the mechanical system shown in the following figure is...
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...
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 =...
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 = 1 N-s/m fr2 M1=1 kg = 2 N-s/m M2 -1 kg 13 = 1 N-s/m 1. Find the differential equations relating input force f(t) and output displacement xi(t) and x2(C) in the system. (40 marks) (Hint: K, fy and M are spring constant, friction coefficient and mass respectively) 2. Determine the transfer function G(s)= X1(s)/F(s) (20 marks)
4. Consider the mechanical system shown below with a spring with stiffness, k (N/m), in parallel...
4. Consider the mechanical system shown below with a spring with stiffness, k (N/m), in parallel with a viscous damper with coefficient, h (Nós/m) and an externally applied force, Fexi(t) (N). u(t) a. Find the equation that relates the applied force, Fext(t) and the displacement, u(t). b. If the spring component has a stiffness of k = 75 N/m, the damper component has coefficient h = 50 N s/m and the externally applied force is a constant 4.5 N applied...
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and it...
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and its displacement is measured via r(t), whilst k and c are the spring and damper constants, respectively x(t) Figure 8: A spring-mass-damper system. a) Obtain the differential equation that relates the input force F, to the measured dis- (6 marks) placement x(t) for the system in Figure 8. b) Draw the block diagram representation of the system in Figure 8. c) Based on...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
Question 3) Consider the mechanical system shown in figure, T(t) is the torque applied to shaft...
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 mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is...
Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is applied to the right shaft but the angular position of the left shaft is to be controlled, k is the stiffness of the linear rotary spring and b is the viscous friction coefficient of the ball bearing that supports the right shaft and acts as a linear viscous damper with rotary motion. The left shaft is only supported by the right shaft, so there...
Figure below shows the time response of the system mechanical figure above to a force in step of 8.5 N. Following the...
Figure below shows the time response of the system mechanical figure above to a force in step of 8.5 N.
Following the analysis of the system in the figure above
a) Determine the transfer function X(s)/F(s) of the system and give the standard form of the latter.
b) Based on the response of this system at 8.5 N, determine the , and parameters of the mechanical system.
c) By combining the results found previously, determine the value of the three...
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force that is a function of its extension. A damper exerts a force that is a function of the velocity of the piston. Assume that the spring and the damper are both linear. (1) We want to describe the relation between the external force F(t) and the position yt) of the mass. Give the differential equation relating F(t) and y(t). Define this carefully as a...
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...
For a mass-spring-damper mechanical systems shown below, x200) K1-1 N/m 0000 -X,(0) K-1 N/m 00004 = 1 N-s/m fr2 M1=1 kg = 2 N-s/m M2 -1 kg 13 = 1 N-s/m 1. Find the differential equations relating input force f(t) and output displacement xi(t) and x2(C) in the system. (40 marks) (Hint: K, fy and M are spring constant, friction coefficient and mass respectively) 2. Determine the transfer function G(s)= X1(s)/F(s) (20 marks)
4. Consider the mechanical system shown below with a spring with stiffness, k (N/m), in parallel with a viscous damper with coefficient, h (Nós/m) and an externally applied force, Fexi(t) (N). u(t) a. Find the equation that relates the applied force, Fext(t) and the displacement, u(t). b. If the spring component has a stiffness of k = 75 N/m, the damper component has coefficient h = 50 N s/m and the externally applied force is a constant 4.5 N applied...
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and its displacement is measured via r(t), whilst k and c are the spring and damper constants, respectively x(t) Figure 8: A spring-mass-damper system. a) Obtain the differential equation that relates the input force F, to the measured dis- (6 marks) placement x(t) for the system in Figure 8. b) Draw the block diagram representation of the system in Figure 8. c) Based on...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
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 mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is applied to the right shaft but the angular position of the left shaft is to be controlled, k is the stiffness of the linear rotary spring and b is the viscous friction coefficient of the ball bearing that supports the right shaft and acts as a linear viscous damper with rotary motion. The left shaft is only supported by the right shaft, so there...
Figure below shows the time response of the system mechanical figure above to a force in step of 8.5 N.
Following the analysis of the system in the figure above
a) Determine the transfer function X(s)/F(s) of the system and give the standard form of the latter.
b) Based on the response of this system at 8.5 N, determine the , and parameters of the mechanical system.
c) By combining the results found previously, determine the value of the three...
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