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This is a differential equation
result of 5. Physical spring-mass systems almost always have some damping...
5. A 2 kg mass is attached to a spring whose constant is 30 N/m, and the entire system is submerg...
5. A 2 kg mass is attached to a spring whose constant is 30 N/m, and the entire system is submerged in a liquid that imparts a damping force equal to 12 times the instaataneous velocity (a) Write the second-order linear differential equation to umodel the motion (b) Convert the second-order linear differential equation from part (a) to a first-order linear system (c) Classify the critical (equilibrium) point (0.0) (d) Sketch the phase portrait (e) Indicate the initial condition x(0)-(...
Spring mass damper system with forced response, the forced system given by the equation For damping...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertic...
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The gravitational force is mg dowswards, where g- 9.8m is acceleration due to gravity, measured...
The position x of a mass m attached to a spring obeys the differential equation i...
The position x of a mass m attached to a spring obeys the differential equation i + yi + w?x = 0 where y 2w. a) (2 marks) Write down expressions for the forces on the mass due to (i) the spring, and (ii) damping. (3 marks) Using a trial solution x = Ae"', show that a = --y/2 ± (y2/4 - «2)1/2 b) c) (4 marks) Show, by finding wd, that the solution is a damped oscillation of the...
5) Given the following, solve the differential equation for a mass on a spring. A 96...
5) Given the following, solve the differential equation for a mass on a spring. A 96 pound weight hangs from a spring. The damping coefficient is 6 slugs/second and the spring constant is 3 pounds/foot. There is an applied force of 8cos3t pounds. The weight starts from the equilibrium position with an upward velocity of 6 feet/second. (In other words, x(0) = 0 and x'(O) = -6)
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....
In a hurry to digest this . Tks for the help (thumb up) 2. A mass of m kilograms (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to t...
In a hurry to digest this . Tks for the help (thumb up)
2. A mass of m kilograms (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixed to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The...
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1 = 1kg, c = 5N.s/m, k = 4 N/m F(t) = 2N And x'...
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1 = 1kg, c = 5N.s/m, k = 4 N/m F(t) = 2N And x'(0)=x(0)=0 Find the solution of this differential equation using Laplace transforms. F(t) 7m
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1...
A brick is attached to a horizontal spring and is able to slide back and forth....
A brick is attached to a horizontal spring and is able to slide back and forth. The mass of the brick is m= 2 kg., the spring constant is k = 40 N./m., and friction provides a resistive force equal (in N.) to c= 16 times the velocity of the brick (in m./sec.). a) Formulate a differential equation that models this problem, using 1 = time (in secs.) and x(t) = displacement (to the right of the equilibrium position, in...
5. A 2 kg mass is attached to a spring whose constant is 30 N/m, and the entire system is submerged in a liquid that imparts a damping force equal to 12 times the instaataneous velocity (a) Write the second-order linear differential equation to umodel the motion (b) Convert the second-order linear differential equation from part (a) to a first-order linear system (c) Classify the critical (equilibrium) point (0.0) (d) Sketch the phase portrait (e) Indicate the initial condition x(0)-(...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
A mass of m kilograams (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixced to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The gravitational force is mg dowswards, where g- 9.8m is acceleration due to gravity, measured...
The position x of a mass m attached to a spring obeys the differential equation i + yi + w?x = 0 where y 2w. a) (2 marks) Write down expressions for the forces on the mass due to (i) the spring, and (ii) damping. (3 marks) Using a trial solution x = Ae"', show that a = --y/2 ± (y2/4 - «2)1/2 b) c) (4 marks) Show, by finding wd, that the solution is a damped oscillation of the...
5) Given the following, solve the differential equation for a mass on a spring. A 96 pound weight hangs from a spring. The damping coefficient is 6 slugs/second and the spring constant is 3 pounds/foot. There is an applied force of 8cos3t pounds. The weight starts from the equilibrium position with an upward velocity of 6 feet/second. (In other words, x(0) = 0 and x'(O) = -6)
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....
In a hurry to digest this . Tks for the help (thumb up)
2. A mass of m kilograms (kg) is mounted on top of a vertical spring. The spring is L metres long when disengaged and the end not attached to the mass is fixed to the ground. The mass moves vertically up and down, acted on by gravity, the restoring force T of the spring and the damping force R due to friction: see the diagram below The...
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1 = 1kg, c = 5N.s/m, k = 4 N/m F(t) = 2N And x'(0)=x(0)=0 Find the solution of this differential equation using Laplace transforms. F(t) 7m
The following differential equation is the equation of motion for an ideal spring-mass system with damping and an external force F(t) m. x C. x If m1...
A brick is attached to a horizontal spring and is able to slide back and forth. The mass of the brick is m= 2 kg., the spring constant is k = 40 N./m., and friction provides a resistive force equal (in N.) to c= 16 times the velocity of the brick (in m./sec.). a) Formulate a differential equation that models this problem, using 1 = time (in secs.) and x(t) = displacement (to the right of the equilibrium position, in...
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