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The suspension of a modified baby bouncer is modelled by a model spring 9 A with...
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...
9. A mechanical component can be modelled as a pendulum with a torsional damper of coefficient,...
9. A mechanical component can be modelled as a pendulum with a torsional damper of coefficient, c, at its oO hinge as shown in Figure Q.9. Stiffness in the system is modelled by a spring of stiffness, k, located at the midpoint of the light bar of length 1. The pendulum is free to rotate about the hinge O and has bob-mass m a) Show that the equation of motion of the system for small angular displacements, 6, is given...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
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...
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...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass of the handle is negligi- ble (only 1 FBD is necessary). Consider the displacement (t) to be the input to the system and the cart displacement az(t) to be the output. You may assume negligible drag. MwSpring-Damper System M0 Problem 3 Repeat problem 2, but with the following differences: • Assume the mass of the handle m, is not equal to zero. You may...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two per...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
Question 8 (Revision: Unit 9) - 5 marks A particle of mass 2 kg is attached...
Question 8 (Revision: Unit 9) - 5 marks A particle of mass 2 kg is attached to one end of a model spring that is hanging vertically from a fixed point 0. The spring has stiffness 4 Nm-1 and natural length 1 m. The system is oscillating in a vertical line with the particle below 0. In this question use the approximation that the magnitude of the acceleration due to gravity is 10 ms-2. Take the point O as the...
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...
9. A mechanical component can be modelled as a pendulum with a torsional damper of coefficient, c, at its oO hinge as shown in Figure Q.9. Stiffness in the system is modelled by a spring of stiffness, k, located at the midpoint of the light bar of length 1. The pendulum is free to rotate about the hinge O and has bob-mass m a) Show that the equation of motion of the system for small angular displacements, 6, is given...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
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...
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...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass of the handle is negligi- ble (only 1 FBD is necessary). Consider the displacement (t) to be the input to the system and the cart displacement az(t) to be the output. You may assume negligible drag. MwSpring-Damper System M0 Problem 3 Repeat problem 2, but with the following differences: • Assume the mass of the handle m, is not equal to zero. You may...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
Question 8 (Revision: Unit 9) - 5 marks A particle of mass 2 kg is attached to one end of a model spring that is hanging vertically from a fixed point 0. The spring has stiffness 4 Nm-1 and natural length 1 m. The system is oscillating in a vertical line with the particle below 0. In this question use the approximation that the magnitude of the acceleration due to gravity is 10 ms-2. Take the point O as the...
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