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5) Given the following, solve the differential equation for a mass on a spring. A 96...
Given the following, solve the differential equation for a mass on a spring. A 96 pound...
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'(0) = -6)
6. A 32-pound object stretches a spring 8 feet to reach equilibrium. The object is then...
6. A 32-pound object stretches a spring 8 feet to reach equilibrium. The object is then pulled to a point that is I foot below the equilibrium position and released from with an upward velocity of 6 feet per second Assume a damping force of 5. What is the position of the object when it attains its maximum displacement above the equilibrium position? Express your answer to 4 decimal places
I need the correct u(t). Ibs stretches a spring 4 inches what is the spring constant?...
I need the correct u(t).
Ibs stretches a spring 4 inches what is the spring constant? If the mass has a velocity of 6 ft/sec and this results in a viscous resistance of 117 lbs what is the damping coefficient? If a mass weighing Assume 32lb = 1 slug Preview slugs a. What is the mass of the object? 15 lb sec b. What is the damping coefficient? c19s . What is the spring constant? k = 144 ft n...
A 32 pound weight is attached to the lower end of a coiled spring suspended from the ceiling. The...
A 32 pound weight is attached to the lower end of a coiled spring suspended from the ceiling. The spring constant for the spring is 9. At time t = 0, the weight is positioned Sqrt(3) feet below equilibrium and given an upward velocity of 3 feet per second. Determine the equation of motion of the weight as a function of time. Find the amplitude of the motion. Find the period of the motion. Find the phase angle. Determine the...
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. ...
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. The medium offers a damping force equal to 0.5 times the instantaneous velocity. Find the equation of motion if the mass is released from rest at a position 18 inches above the equilibrium.
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. The medium offers a damping...
1. A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds...
1. A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force that is equal to 0.4 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (b)...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 feet. The entire system...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 feet. The entire system is placed in a medium that offers a damping force numerically equivalent to twice the instantaneous velocity. The mass is initially released from a point 1/2 foot above the equilibrium point with a downward velocity of 5 ft/sec. (a) (6 points) Write the differential equation for the mass/spring system and identify the initial conditions. 7 5. (b) (12 points) Solve the IVP in part...
Solve it with matlab 25.16 The motion of a damped spring-mass system (Fig. P25.16) is described...
Solve it with matlab
25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d’x dx ++ kx = 0 m dr dt where x = displacement from equilibrium position (m), t = time (s), m 20-kg mass, and c = the damping coefficient (N · s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m....
Differential Equation problem We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed t...
Differential Equation problem
We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed to come to equilibrium. The mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second. Let y(t) represent the displacement of the mass above the equilibrium position t seconds...
Problem #6: A 144lb weight stretches a spring 18 feet. The weight hangs vertically from the...
Problem #6: A 144lb weight stretches a spring 18 feet. The weight hangs vertically from the spring and a damping force numerically equal to 12 times the instantaneous velocity acts on the system. The weight is released from 9 feet above the equilibrium position with a downward velocity of 39 fts. (a) Determine the time (in seconds) at which the mass passes through the equilibrium position. (b) Find the time in seconds) at which the mass attains its extreme displacement...
6. A 32-pound object stretches a spring 8 feet to reach equilibrium. The object is then pulled to a point that is I foot below the equilibrium position and released from with an upward velocity of 6 feet per second Assume a damping force of 5. What is the position of the object when it attains its maximum displacement above the equilibrium position? Express your answer to 4 decimal places
I need the correct u(t).
Ibs stretches a spring 4 inches what is the spring constant? If the mass has a velocity of 6 ft/sec and this results in a viscous resistance of 117 lbs what is the damping coefficient? If a mass weighing Assume 32lb = 1 slug Preview slugs a. What is the mass of the object? 15 lb sec b. What is the damping coefficient? c19s . What is the spring constant? k = 144 ft n...
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. The medium offers a damping force equal to 0.5 times the instantaneous velocity. Find the equation of motion if the mass is released from rest at a position 18 inches above the equilibrium.
1. A mass weighing 8 pounds is attached to a 4 foot long spring and stretches it to 8 feet long. The medium offers a damping...
1. A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force that is equal to 0.4 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (b)...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 feet. The entire system is placed in a medium that offers a damping force numerically equivalent to twice the instantaneous velocity. The mass is initially released from a point 1/2 foot above the equilibrium point with a downward velocity of 5 ft/sec. (a) (6 points) Write the differential equation for the mass/spring system and identify the initial conditions. 7 5. (b) (12 points) Solve the IVP in part...
Solve it with matlab
25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d’x dx ++ kx = 0 m dr dt where x = displacement from equilibrium position (m), t = time (s), m 20-kg mass, and c = the damping coefficient (N · s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m....
Differential Equation problem
We know that a force of 2.8 Newtons is required to stretch a certain spring 0.7 meters beyond its natural length. A 1.44-kg mass is attached to this spring and allowed to come to equilibrium. The mass-spring system is then set in motion by applying a push in the upward direction that gives the mass an initial velocity of 1.04 meters per second. Let y(t) represent the displacement of the mass above the equilibrium position t seconds...
Problem #6: A 144lb weight stretches a spring 18 feet. The weight hangs vertically from the spring and a damping force numerically equal to 12 times the instantaneous velocity acts on the system. The weight is released from 9 feet above the equilibrium position with a downward velocity of 39 fts. (a) Determine the time (in seconds) at which the mass passes through the equilibrium position. (b) Find the time in seconds) at which the mass attains its extreme displacement...
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