Question

In: Physics

A mass of 35 pounds of weight causes a spring to stretch 10 feet, if the...

A mass of 35 pounds of weight causes a spring to stretch 10 feet, if the medium surrounding the system has a damping coefficient, that is, it is equivalent to 5 times the instantaneous speed and the weight is released from a point located at 15 inches below the equilibrium position with an initial velocity of 1 foot per second downwards. A) Derive the differential equation that models the mass-spring system. b) Calculate the displacements (t) at all times “t” c) Write the mass-spring displacements alternatively.

Solutions

Expert Solution

genius_generous answered 2 years ago
Next > < Previous

Related Solutions

A mass weighing 8 pounds stretches a spring 4 feet. The medium through the mass moves...
A mass weighing 8 pounds stretches a spring 4 feet. The medium through the mass moves offers a damping force numerically equal to sqrt(2) times the instantaneous velocity. Find the equation of motion if mass is released from equilibrium position with a downward velocity of 5 ft/s. Find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant? The acceleration of gravity is g = 32...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 7 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 25 cos(3t). (Use g = 32 ft/s2 for the acceleration...
A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from...
A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from a point 1 foot below equilibrium with an upward velocity of 4 ft/s. (a) Find the equation of motion (b) In correct units, what are the amplitude, period, and frequency of this simple harmonic motion? (c) What is the velocity of the mass at ? = 3? 16 seconds? (d) Find the first three times that the velocity is zero, expressed both in exact...
A mass weighing 32 pounds stretches a spring 16 feet. The mass is initially released from...
A mass weighing 32 pounds stretches a spring 16 feet. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion if the mass is driven by an external force equal to f(t)=10cos(3t).
A) A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released...
A) A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass id riven by an external force equal to f(t) = 20 cos 3t use g=32 ft/s^2 for the acceleration due to...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 7 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 25 cos 3t. (Use g = 32 ft/s2 for the...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released...
A mass weighing 16 pounds stretches a spring 8 3 feet. The mass is initially released from rest from a point 5 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1 2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 3 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 10 cos(3t). (Use g = 32 ft/s2 for the acceleration due to...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 5 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration due to...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from...
A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration due to...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT