A mass of 2 kg stretches a spring 0.1 m. At time t= 0 the mass...
A mass of 2 kg stretches a spring 0.1 m. At time t= 0 the mass is released from its equilibrium position with a downward velocity of 1 m/s. Air resistance adds a damping force equal to one fifth of the velocity of the mass. Set up an initial value problem for the position x(t) of the mass at time t. Determine whether the system is overdamped, underdamped or critically damped. You can assume the acceleration of gravity g equals 10 m/s^2. Explicitly state your choice of a coordinate system for the problem (axis, direction, origin)
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A mass weighing 4 pounds stretches a spring 6 inches. At time t = 0, the...
A mass weighing 4 pounds stretches a spring 6 inches. At time t = 0, the weight is then struck to set it into motion with an initial velocity of 2 ft/sec, directed downward. Determine the equations of motion for the position and the velocity of the weight. Find the amplitude, period, and frequency of the position (displacement). A 4-lb weight stretches a spring 1 ft. If the weight moves in a medium where the magnitude of the damping force...
plz print your result -1 points МУ Not A mass weighing 3V 10 N stretches a spring 2 m. The mass is attached to a dashpot device that offers a damping force numerically equal to β (B > 0) times the...
plz print your result
-1 points МУ Not A mass weighing 3V 10 N stretches a spring 2 m. The mass is attached to a dashpot device that offers a damping force numerically equal to β (B > 0) times the instantaneous velocity Determine the values of the damping constant B so that the subsequent motion is overdamped, critically damped, and underdamped. (If an answer is an interval, use interval notation. Use g 9.8 m/s2 for the acceleration due to...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is then submerged in a liquid that inparts a damping force equal to 4 tines the instantansous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force t)4t-3) is applied. (a) Write (t), the external force, as a piecewise function and sketch its graph b) Write the initial-value problem (c)Solve...
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...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 fort. The entire system...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 fort. 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 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...
Consider a mass-spring-dashpot system in which the mass is m = 4 lb-sec^2/ft, the damping constant...
Consider a mass-spring-dashpot system in which the mass is m = 4 lb-sec^2/ft, the damping constant is c =24 lb-sec/ft, and the spring constant is k=52lb/ft. The motion is free damped motion and the mass is set in motion with initial position x0=5ft and the initial velocity v0= -7ft/sec. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped.
A mass of 2 kg stretches a spring 40 cm. The mass is pulled downward 1m...
A mass of 2 kg stretches a spring 40 cm. The mass is pulled downward 1m and released with an upwards velocity of 2m/s. Assuming there is no damping and that^1 the acceleration due to gravity is g = 10m/s^2, determine the position u(t) of the mass at time t, as well as the amplitude, period, frequency, and phase. Provide a rough sketch of the graph of the solution.
(1 point) A mass weighing 8 lb stretches a spring 3 in. Suppose the mass is...
(1 point) A mass weighing 8 lb stretches a spring 3 in. Suppose the mass is displaced an additional 11 in in the positive (downward) direction and then released with an initial upward velocity of 2 ft/s. The mass is in a medium, that exerts a viscuouse resistance of 1 lb when the mass has a velocity of 4 ft/s. Assume g 32 ft/s is the gravitational acceleration (a) Find the mass m (in lb.s/ft) (b) Find the damping coefficient...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
A mass weighing 4 pounds stretches a spring 6 inches. At time t = 0, the weight is then struck to set it into motion with an initial velocity of 2 ft/sec, directed downward. Determine the equations of motion for the position and the velocity of the weight. Find the amplitude, period, and frequency of the position (displacement). A 4-lb weight stretches a spring 1 ft. If the weight moves in a medium where the magnitude of the damping force...
plz print your result
-1 points МУ Not A mass weighing 3V 10 N stretches a spring 2 m. The mass is attached to a dashpot device that offers a damping force numerically equal to β (B > 0) times the instantaneous velocity Determine the values of the damping constant B so that the subsequent motion is overdamped, critically damped, and underdamped. (If an answer is an interval, use interval notation. Use g 9.8 m/s2 for the acceleration due to...
6. A mass of 2 kilogram is attached to a spring whose constant is 4 N/m, and the entire system is then submerged in a liquid that inparts a damping force equal to 4 tines the instantansous velocity. At t = 0 the mass is released from the equilibrium position with no initial velocity. An external force t)4t-3) is applied. (a) Write (t), the external force, as a piecewise function and sketch its graph b) Write the initial-value problem (c)Solve...
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...
5. (20 points) A mass weighing 8 pounds stretches a spring 1.6 fort. 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 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...
A mass of 2 kg stretches a spring 40 cm. The mass is pulled downward 1m and released with an upwards velocity of 2m/s. Assuming there is no damping and that^1 the acceleration due to gravity is g = 10m/s^2, determine the position u(t) of the mass at time t, as well as the amplitude, period, frequency, and phase. Provide a rough sketch of the graph of the solution.
(1 point) A mass weighing 8 lb stretches a spring 3 in. Suppose the mass is displaced an additional 11 in in the positive (downward) direction and then released with an initial upward velocity of 2 ft/s. The mass is in a medium, that exerts a viscuouse resistance of 1 lb when the mass has a velocity of 4 ft/s. Assume g 32 ft/s is the gravitational acceleration (a) Find the mass m (in lb.s/ft) (b) Find the damping coefficient...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
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