For the second part, please use method of undetermined coefficient
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For the second part, please use method of undetermined
coefficient
The suspension system in a car...
Part B (Based off week 4/6 workshop content) The rear suspension of a mountain bike consists of a...
Can you help with Q5?
Part B (Based off week 4/6 workshop content) The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper systemm r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by dtm dtm 7m where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be model...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system. r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by dt m dt m where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and r(t) is the downward displacement of the mass. 2. Find the...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be model...
Please i need help with question 4 and 5
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and x(t) is the downward displacement of...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and x(t) is the downward displacement of the mass. 2. Find the homogenous solution, xh, to...
5. Solve the linear, constant coefficient ODE y" – 3y' + 2y = 0; y(0) =...
5. Solve the linear, constant coefficient ODE y" – 3y' + 2y = 0; y(0) = 0, y'(0) = 1. 6. Solve the IVP with Cauchy-Euler ODE x2y" - 4xy' + 6y = 0; y(1) = 2, y'(1) = 0. 7. Given that y = Ge3x + cze-5x is a solution of the homogeneous equation, use the Method of Undetermined Coefficients to find the general solution of the non-homogeneous ODE " + 2y' - 15y = 3x 8. A 2...
1. A suspension system shown in the figure is modified by adding two additional springs each with a spring constant of k, kN/m in addition to the other existing three springs with k 90 kN/m each....
1. A suspension system shown in the figure is modified by adding two additional springs each with a spring constant of k, kN/m in addition to the other existing three springs with k 90 kN/m each. The design also adds two additional dampers in addition to the two existing dampers each with the same viscous damping coefficient c (= 4000 Ns/m). The viscous damping ratiofor the underdamped system, 7 is 0.95. The mass of the system, m = 150 kg....
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1....
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1. An active suspension element produces an input force F. Draw a free-body diagram for the sprung mass m, and hence derive a differential equation relating the input force F to the sprung mass displacement x. (a) (5 marks) (b) Assuming a mass m-250kg, spring coefficient k 100Nm-1 and damping coefficient of c-50Nsm1, show that the transfer function from the input force F to the...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use a free-body diagram and apply Newton's 2nd Law to show that the upward displacement of the mass, r(t), can be modelled with the ODE da da mdt2 + cat + kz = F(t) where k is the spring coefficient and c is the damping coefficient. = 2 kg, c = For the remainder of the questions, use the following values: m 8 Ns/m, k...
An engineering company is designing and testing a car suspension system. The system has a convent...
Create a MATLAB script
An engineering company is designing and testing a car suspension system. The system has a conventional suspension design, consisting of a shock-absorber and spring at vertical speed (ie. up and down motion) of the wheel, and the spring's resistance is proportional to the vertical displacement of the wheel. The company would like to investigate how the actual performance of the suspension system compares to that of theory. Dynamic theory states that the equation of motion of...
. Shies Paragraph HW 2-ODE Application Part Al Mass spring damper system as represented in the...
.
Shies Paragraph HW 2-ODE Application Part Al Mass spring damper system as represented in the figure. If the block has a mass of 0.25 g started vibrated freely from rest at the equilibrium position, the spring is a massless with a stiffness of (N/m) and the damping coefficient ciNs/m such that is less than 4 Na/m. Find all possible equations of motion (t) for the block Part If two DC motors applied an external force (t) = n(t) and...
Can you help with Q5?
Part B (Based off week 4/6 workshop content) The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper systemm r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by dtm dtm 7m where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system. r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by dt m dt m where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and r(t) is the downward displacement of the mass. 2. Find the...
Please i need help with question 4 and 5
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and x(t) is the downward displacement of...
The rear suspension of a mountain bike consists of a spring suspended in a fluid and can be modelled as a spring and damper system r(t) 1. Draw a free body diagram of the scenario above and show that the resulting ODE is given by where c is the damping constant, k is the spring stiffness, r(t) is the force pressing into the frame and x(t) is the downward displacement of the mass. 2. Find the homogenous solution, xh, to...
5. Solve the linear, constant coefficient ODE y" – 3y' + 2y = 0; y(0) = 0, y'(0) = 1. 6. Solve the IVP with Cauchy-Euler ODE x2y" - 4xy' + 6y = 0; y(1) = 2, y'(1) = 0. 7. Given that y = Ge3x + cze-5x is a solution of the homogeneous equation, use the Method of Undetermined Coefficients to find the general solution of the non-homogeneous ODE " + 2y' - 15y = 3x 8. A 2...
1. A suspension system shown in the figure is modified by adding two additional springs each with a spring constant of k, kN/m in addition to the other existing three springs with k 90 kN/m each. The design also adds two additional dampers in addition to the two existing dampers each with the same viscous damping coefficient c (= 4000 Ns/m). The viscous damping ratiofor the underdamped system, 7 is 0.95. The mass of the system, m = 150 kg....
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1. An active suspension element produces an input force F. Draw a free-body diagram for the sprung mass m, and hence derive a differential equation relating the input force F to the sprung mass displacement x. (a) (5 marks) (b) Assuming a mass m-250kg, spring coefficient k 100Nm-1 and damping coefficient of c-50Nsm1, show that the transfer function from the input force F to the...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use a free-body diagram and apply Newton's 2nd Law to show that the upward displacement of the mass, r(t), can be modelled with the ODE da da mdt2 + cat + kz = F(t) where k is the spring coefficient and c is the damping coefficient. = 2 kg, c = For the remainder of the questions, use the following values: m 8 Ns/m, k...
Create a MATLAB script
An engineering company is designing and testing a car suspension system. The system has a conventional suspension design, consisting of a shock-absorber and spring at vertical speed (ie. up and down motion) of the wheel, and the spring's resistance is proportional to the vertical displacement of the wheel. The company would like to investigate how the actual performance of the suspension system compares to that of theory. Dynamic theory states that the equation of motion of...
.
Shies Paragraph HW 2-ODE Application Part Al Mass spring damper system as represented in the figure. If the block has a mass of 0.25 g started vibrated freely from rest at the equilibrium position, the spring is a massless with a stiffness of (N/m) and the damping coefficient ciNs/m such that is less than 4 Na/m. Find all possible equations of motion (t) for the block Part If two DC motors applied an external force (t) = n(t) and...
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