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1. A mass m, initially at rest, is subject to a constant applied force F. After the mass has trav...
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....
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s...
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s is stopped at the end of the tracks by a spring-damper system, as shown below. If the stiffness of the spring is k= 40 N/mm and the damping constant c 20 N-s/mm, determine (a) the maximum displacement of the car after engaging the springs and damper, (b) the time taken to reach maximum displacement k2 P 0000 k/2
1) A railroad car of mass...
6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' +...
6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey is changed...
a-d please 6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy"...
a-d please
6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey...
6) The 18 kg mass of a spring-mass system is initially at rest. At time =...
6) The 18 kg mass of a spring-mass system is initially at rest. At time = 0, a 400 N force is applied (toward the right). Spring constant is 100 kN / m, and the viscous damping coefficient is 520 Ns/m Determine the transient response F = (400 N) 1(t) Delay time [HINT: may need to a) graphing calculator, fixed point iteration; or calculator equation solver] b) c) use a m Peak time Maximum overshoot (in mm)
6) The 18...
Time (s) Problem 4 (16 pts) A sailing ship of mass, m, is initially at rest,...
Time (s) Problem 4 (16 pts) A sailing ship of mass, m, is initially at rest, i.e. V(O) strong wind arises of magnitude and keep push the ship. 0. At time Vo = 40m/s Assume that the force of the wind on the sails in the direction of travel is given by Fw(t) = Bw [V - v(t)] Assume that the viscous drag of the water on the ship is given by a. (4 pts) Formulate a differential equation that...
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)-(...
I've got parts a-c and understand them. However, I do not understand the rest of the problem and how to solve for th...
I've got parts a-c and
understand them. However, I do not understand the rest of the
problem and how to solve for the answers in parts d and e. Any
explanation would be helpful.
(1 point) A mass of 4 kg stretches a spring 40 cm. The mass is acted on by an external force of F(t) = 97 cos(0.5t) N and moves in a medium that imparts a viscous force of 8 N when the speed of the mass...
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...
4. (20 points) A mass pring system has a mass of kg, a damping constant of...
4. (20 points) A mass pring system has a mass of kg, a damping constant of kg/sec and a spring constant of 15 kg/sec2. There is no external force. The system is started in motion at y 4 meters with an initial velocity of 3 m/s in the downward direction. a) Find the differential equation and the initial conditions that describe the motion of this system. b) Solve the resulting initial value problem. c) Is the spring system overdamped, underdamped...
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....
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s is stopped at the end of the tracks by a spring-damper system, as shown below. If the stiffness of the spring is k= 40 N/mm and the damping constant c 20 N-s/mm, determine (a) the maximum displacement of the car after engaging the springs and damper, (b) the time taken to reach maximum displacement k2 P 0000 k/2
1) A railroad car of mass...
6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey is changed...
a-d please
6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey...
6) The 18 kg mass of a spring-mass system is initially at rest. At time = 0, a 400 N force is applied (toward the right). Spring constant is 100 kN / m, and the viscous damping coefficient is 520 Ns/m Determine the transient response F = (400 N) 1(t) Delay time [HINT: may need to a) graphing calculator, fixed point iteration; or calculator equation solver] b) c) use a m Peak time Maximum overshoot (in mm)
6) The 18...
Time (s) Problem 4 (16 pts) A sailing ship of mass, m, is initially at rest, i.e. V(O) strong wind arises of magnitude and keep push the ship. 0. At time Vo = 40m/s Assume that the force of the wind on the sails in the direction of travel is given by Fw(t) = Bw [V - v(t)] Assume that the viscous drag of the water on the ship is given by a. (4 pts) Formulate a differential equation that...
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)-(...
I've got parts a-c and
understand them. However, I do not understand the rest of the
problem and how to solve for the answers in parts d and e. Any
explanation would be helpful.
(1 point) A mass of 4 kg stretches a spring 40 cm. The mass is acted on by an external force of F(t) = 97 cos(0.5t) N and moves in a medium that imparts a viscous force of 8 N when the speed of the mass...
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...
4. (20 points) A mass pring system has a mass of kg, a damping constant of kg/sec and a spring constant of 15 kg/sec2. There is no external force. The system is started in motion at y 4 meters with an initial velocity of 3 m/s in the downward direction. a) Find the differential equation and the initial conditions that describe the motion of this system. b) Solve the resulting initial value problem. c) Is the spring system overdamped, underdamped...
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