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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 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 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...
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 suspension of a modified baby bouncer is modelled by a model spring 9 A with...
The suspension of a modified baby bouncer is modelled by a model spring 9 A with stiffness k1 and a model damper T A with damping coefficient r. The seat is tethered to the ground, and this tether is modelled by a second model springAS with stiffness k2. Model the combination of baby and seat as a particle of mass m at a point A that is a distance r above floor level. The bouncer is suspended from a fixed...
PLEASE READ CAREFULLY TASK GIVEN BELOW AND ANSWERS THE QUESTIONS WHICH BEEN ASKED A vehicle suspension...
PLEASE READ CAREFULLY TASK GIVEN BELOW AND ANSWERS THE QUESTIONS WHICH BEEN ASKED A vehicle suspension system can be modelled by the block diagram shown in Figure 1 below: Body mas:s 12 er of s cmicen G, Roac rgut Figure 1: Block diogrom of vehicle suspension system In this block diagram, the variation in the road surface height r as the vehicle moves is the input to the system. The tyre is modelled by the spring and dashpot (damping) system...
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...
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following....
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following. The mass m 1, damping coetfic e initial position y(o) O, and the initial velocity i constant k 3 and force 10, all are in appropriate units. Th 1, spring zero, within the time range of O to 20 unit of time, use Matlab find the solution of function y(t)? Hint: you need to convert the 2nd order ODE into two 1st order ODEs....
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 a mass-spring-damper system whose motion is described by the following system of differe...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
Suppose a mass of 1 kg is attached to a spring with spring constant k =...
Suppose a mass of 1 kg is attached to a spring with spring constant k = 2, and rests at equilibrium position. Starting at t = 0, an external force of f(t) = e t is applied to the system. Suppose the surrounding medium offers a damping force numerically equal to β times the instantaneous velocity, where β > 0 is some given number. (a) What is the IVP governing this harmonic motion. (b) For what value(s) of β will...
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 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...
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 suspension of a modified baby bouncer is modelled by a model spring 9 A with stiffness k1 and a model damper T A with damping coefficient r. The seat is tethered to the ground, and this tether is modelled by a second model springAS with stiffness k2. Model the combination of baby and seat as a particle of mass m at a point A that is a distance r above floor level. The bouncer is suspended from a fixed...
PLEASE READ CAREFULLY TASK GIVEN BELOW AND ANSWERS THE QUESTIONS WHICH BEEN ASKED A vehicle suspension system can be modelled by the block diagram shown in Figure 1 below: Body mas:s 12 er of s cmicen G, Roac rgut Figure 1: Block diogrom of vehicle suspension system In this block diagram, the variation in the road surface height r as the vehicle moves is the input to the system. The tyre is modelled by the spring and dashpot (damping) system...
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...
Problem Set A Problem 6. (20%) A ordinary differential equation for a mass-damper-spring system is following. The mass m 1, damping coetfic e initial position y(o) O, and the initial velocity i constant k 3 and force 10, all are in appropriate units. Th 1, spring zero, within the time range of O to 20 unit of time, use Matlab find the solution of function y(t)? Hint: you need to convert the 2nd order ODE into two 1st order ODEs....
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 a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
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