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2. For the mechanical system shown below, find the equation that relates settling time of the...
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...
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...
Consider the translational mechanical system shown in the figure. A 1-pound force, f(t), is applied at...
Consider the translational mechanical system shown in the figure. A 1-pound force, f(t), is applied at t = 0. If fo = 1, find K and M such that the response is characterized by a 4- second settling time and a 1-second peak time. Also, what is the resulting percent overshoot? ft
4. The mechanical system below represents a weight machine often used by Olympic downhill skiers to...
4. The mechanical system below represents a weight machine often used by Olympic downhill skiers to increase lower body strength. The skier attempts to displace a mass, M, by applying vertical force f(t). Friction occurs between the mass and vertical surfaces with frictional coefficients 7, and 12. 2, N = 2 = 1 Ns/m D, - R = 3 Ns/m K = K₂ * 13 N/m м. fit 40 M - 2kg Assuming that the skier is training in a...
s) Given the following rotational mechanical system, hot relates the input variable T (applied torque) to...
s) Given the following rotational mechanical system, hot relates the input variable T (applied torque) to the output a) Write the differential equation that re variable angular displacement) b) Convert the differential equatio c) Write the Transfer function of the system (I. w ent the differential equation to Laplace domain assuming initial conditions Zero Consider the following values for the parameters: J - 2 kg-m? (moment of inertial of the mass) D = 0.5 N-m-s/rad (coefficient of friction) K-1 N-m/rad...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
The mechanical system shown in the figure below is excited by a sinusoidal force f(t)-Fi cos(ut...
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...
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)
Problem 2 (25 points) For the rotational mechanical system with gears shown below, find the transfer...
Problem 2 (25 points) For the rotational mechanical system with gears shown below, find the transfer function G(s)-0s(s)/T(s). The gears have inertia and bearing friction as shown T(0) Ji. D N2 N3 2. D2 14. D
Using the force-voltage analogy shown in table 1, obtain a mechanical analogu electrical system shown above...
Using the force-voltage analogy shown in table 1, obtain a mechanical analogu electrical system shown above (4 pts) Table 1. Force-Voltage Analogy Force, p (torque T Mass, m (moment of inertia J) Viscous-friction coefficient, b Spring constant, k Displacement, x (angular displacement 6) Voltage, Inductance, L Resistance, R Reciprocal of capacitance, /C Charge, Velocity (angular velocity b) Current, i
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...
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...
Consider the translational mechanical system shown in the figure. A 1-pound force, f(t), is applied at t = 0. If fo = 1, find K and M such that the response is characterized by a 4- second settling time and a 1-second peak time. Also, what is the resulting percent overshoot? ft
4. The mechanical system below represents a weight machine often used by Olympic downhill skiers to increase lower body strength. The skier attempts to displace a mass, M, by applying vertical force f(t). Friction occurs between the mass and vertical surfaces with frictional coefficients 7, and 12. 2, N = 2 = 1 Ns/m D, - R = 3 Ns/m K = K₂ * 13 N/m м. fit 40 M - 2kg Assuming that the skier is training in a...
s) Given the following rotational mechanical system, hot relates the input variable T (applied torque) to the output a) Write the differential equation that re variable angular displacement) b) Convert the differential equatio c) Write the Transfer function of the system (I. w ent the differential equation to Laplace domain assuming initial conditions Zero Consider the following values for the parameters: J - 2 kg-m? (moment of inertial of the mass) D = 0.5 N-m-s/rad (coefficient of friction) K-1 N-m/rad...
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
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...
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)
Problem 2 (25 points) For the rotational mechanical system with gears shown below, find the transfer function G(s)-0s(s)/T(s). The gears have inertia and bearing friction as shown T(0) Ji. D N2 N3 2. D2 14. D
Using the force-voltage analogy shown in table 1, obtain a mechanical analogu electrical system shown above (4 pts) Table 1. Force-Voltage Analogy Force, p (torque T Mass, m (moment of inertia J) Viscous-friction coefficient, b Spring constant, k Displacement, x (angular displacement 6) Voltage, Inductance, L Resistance, R Reciprocal of capacitance, /C Charge, Velocity (angular velocity b) Current, i
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