Question

In: Advanced Math

A 6 lb weight is placed upon the lower end of a coil spring suspended from...

A 6 lb weight is placed upon the lower end of a coil spring suspended from a fixed beam. The weight comes to rest in its equilibrium position, thereby stretching the spring 4 inches. Then
beginning at t = 0 an external force given by F (t) = 27 sin(4t) − 3 cos(4t) is applied to the system. The resistance of the medium is three times the velocity (in ft/sec). Find the displacement of the weight as a function of time.

Solutions

Expert Solution


Related Solutions

A 12-lb weight is placed upon the lower end of a suspended spring. The weight comes...
A 12-lb weight is placed upon the lower end of a suspended spring. The weight comes to rest in its equilibrium position, stretching the spring by 1.5 inches. The weight is then pushed upward 2 inches above the equilibrium and released at t=0 with an initial velocity downward of 2ft/sec. Assume there is no damping caused by an external force a) Find the displacement of the weight function x(t) as a function of time, b) Determine the amplitude, period, and...
DIFFERENTIAL EQUATIONS An 8-lb weight is attached to the lower end of a coil spring suspended...
DIFFERENTIAL EQUATIONS An 8-lb weight is attached to the lower end of a coil spring suspended from a fixed support. The weight comes to rest in its equilibrium position, thereby stretching the spring 6 in. The weight is then pulled down 9 in. below its equilibrium position and released at t=0. The medium offers a resistance in pounds numerically equal to 4x', where x' is the instantaneous velocity in feet per second. Determine the displacement of the weight as a...
Differential Equations (FREE, UNDAMPED MOTION) A 12-lb weight is placed upon the lower end of a...
Differential Equations (FREE, UNDAMPED MOTION) A 12-lb weight is placed upon the lower end of a coil spring suspended from the ceiling. The weight comes to rest in its equilibrium position, thereby stretching the spring 1.5 in. The weight is then pulled down 2 in. Below its equilibrium position and released from rest at t = 0. Find the displacement of the weight as a function of time; determine the amplitude, period, and the frequency of the resulting motion. Assume...
A 64 pound weight is attached to the lower end of a coiled spring suspended from...
A 64 pound weight is attached to the lower end of a coiled spring suspended from the ceiling. The weight comes to rest at its equilibrium position, thereby stretching the spring 1/2 foot. At time t = 0, the weight is positioned 1 /√3 feet below equilibrium and given a downward velocity of 8 feet per second. (a) Determine the equation of motion of the weight as a function of time. (b) Find the amplitude of the motion. (c) Find...
2. A 6-lb weight is attached to a vertically suspended spring that it stretches 4 in....
2. A 6-lb weight is attached to a vertically suspended spring that it stretches 4 in. and to adashpot that provides 1.5 lb of resistance for every foot per second of velocity.(a) If the weight is pulled down 1 ft below its static equilibrium position and then released from rest at time t = 0, find its position function .(b) Find the frequency, time-varying amplitude, and phase angle of the motion.(Give exact answers for both parts.
A 0.167-kg frame, when suspended from a coil spring, stretches the spring 0.0400 m. A 0.200-kg...
A 0.167-kg frame, when suspended from a coil spring, stretches the spring 0.0400 m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm. Find the maximum distance the frame moves downward from its initial equilibrium position.
A weight is attached to a spring suspended from a beam. At time t = 0,...
A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 7 cm above the ground and released. After that, it bounces up and down between its minimum height of 7 cm and a maximum height of 25 cm, and its height h(t) is a sinusoidal function of time t. It first reaches a maximum height 1.4 seconds after starting. (b) What are the mean, amplitude, phase shift...
A 128-lb weight is attached to a spring having a spring constant of 64 lb/ft. The...
A 128-lb weight is attached to a spring having a spring constant of 64 lb/ft. The weight is started in motion with no initial velocity by displacing it 6 in below the equilibrium position and by simultaneously applying an external force F(t) = 8sin(4t). a. Assuming no air resistance, find the equation of motion. b. What is the long term behavior of the motion? Please use differential equations to solve this
A mass suspended at the end of a light Spring and spring constant K is set...
A mass suspended at the end of a light Spring and spring constant K is set into vertical motion use lagrange's equation to find the equation of motion of the mass
A square plastic chunk with mass 0.750 kg is suspended from the lower end of a...
A square plastic chunk with mass 0.750 kg is suspended from the lower end of a light cord that is 1.66 mm long. The plastic chunk is stay still in the beginning without any motion. A bullet with mass 0.0132 kg is on the way to the plastic chunk with a horizontal velocity v0. The bullet hits the plastic chunk and then embedded in it. After collision, combined bullet and plastic chunk swings on the end of the cord. When...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT