DIfferential Equation Class Problem: A spring is stretched 0.10 m by a force of 3 newtons....

DIfferential Equation Class Problem: A spring is stretched 0.10 m by a force of 3 newtons. A mass of 2 kg is hung from the spring and is also attached to a viscous damper that exerts a force of 3 newtons when the velocity of the mass is 5 m/sec. If the mass is pulled down 0.05 m below its equilibrium position and given an initial downward velocity of 0.10 m/sec, determine its position U at any time T.

Solutions

Expert Solution

Hello dear if any other issues with this solutions please informing me... for my request at least before your negative response please comment I'll help you ..we look forward for your happiness ....thank you ..keep smiling .. :)

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring

PLEASE ANSWER ALL 3 WILL THUMBS UP 1) A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 8 m/s. Find the equation of motion. x(t)=? m 2) Find the charge on the capacitor and the current in an LC-series circuit when L = 0.1 h, C = 0.1 f, E(t) = 100 sin(γt)...

A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is...

A force of 640 newtons stretches a spring 4 meters. A mass of 40 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion.

a. A force of 40 lb is necessary to hold a spring that has been stretched...

a. A force of 40 lb is necessary to hold a spring that has been stretched from its natural length of 10 ft to a length of 15 ft. How much work is done in stretching the spring from 15 ft to a length of 18 ft? (Hint: Use Hook’s Law F = kx, where x represents distance that the spring is stretched or compressed past its natural length) b. A tank full of water has the shape of an...

the force exerted by a spring is given by the equation where F is the force...

the force exerted by a spring is given by the equation where F is the force (in Newtons), xis the displacement of the spring from the equilibrium position (in centimeters), and k is a spring constant Create an Excel worksheet showing force as a function of displacement for two springs whose spring constants are 0.1 N/cm and 0.5 N/cm. Use displacements ranging from 0 to 20 cm (i.e. let x = 0, 1, 2 … 20 cm).

1) A force of 2 pounds is required to hold a spring stretched 0.2 feet beyond...

1) A force of 2 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length? 2) Work of 3 Joules is done in stretching a spring from its natural length to 19 cm beyond its natural length. What is the force (in Newtons) that holds the spring stretched at the same distance (19 cm)?...

3. Solve the following differential equation x^2y’’ − 2xy’ + 5y = 0. A coil spring...

3. Solve the following differential equation x^2y’’ − 2xy’ + 5y = 0. A coil spring is suspended from the ceiling, a 16-lb weight is attached to the end of it, and the weight then comes to rest in its equilibrium position. The mass is in a medium that exerts a viscous resistance of 8 lb when the mass has a velocity of 1 ft/s. It is then pulled down 12 in. below its equilibrium position and released with an...

Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 3 meters by a...

Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 3 meters by a force of 10N, and a dashpot which provides a 4N resistance for each m/s of velocity. The mass is also acted on by a periodic force 5 cos(ωt) for some number ω. • For what value of ω (if any) does practical resonance occur? • If the mass starts at rest, at equilibrium, find a formula for x(t) (in terms of ω), the distance...

A mass m = 1 kg is suspended from a spring that is stretched 1 cm...

A mass m = 1 kg is suspended from a spring that is stretched 1 cm under the influence of the weight of this mass. Now a periodic force is applied external of F (t) = 200 cos (vt) on the mass, which was initially in static balance. Disregarding all friction, get a relationship for position of the mass as a function of time, x (t). Also determine the value of ω which will cause resonance to occur

A spring (k = 100 N/m), which can be stretched or compressed, is placed on a...

A spring (k = 100 N/m), which can be stretched or compressed, is placed on a frictionless table. A 5.00-kg mass is attached to one end of the spring, and the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x = 4.0 cm and releases it from rest. The mass oscillates in simple harmonic motion. (a) Determine the function x(t). (b) Find the magnitudes of maximum velocity...

a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m...

a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m . At t=0.2s, the displacement x=-0.3m, and the velocity v=-2.0m/s a) find the equation of displacement as a function of time b) sketch the displacement as a function of time for the first cycle starting t=0s

Subjects