Question

In: Civil Engineering

Applications of higher order differential equations A spring has one of its ends fixed, and a...

Applications of higher order differential equations

A spring has one of its ends fixed, and a force of 15 N stretches it 20cm. A mass of 4 Kg is attached to the end of the spring, and the system is set in motion with initial position = 60 cm and initial velocity = 1.5 m/s.

(a) Find the spring constant. 
(b) Write a problem of initial conditions for spring stretching, in meters. 
(c) Solve the problem posed in (b). 
(d) Write the solution in the form x = rsen(ωt + θ). 
(e) What are the amplitude, frequency and period of movement?

Solutions

Expert Solution

Ally Wells answered 1 year ago
Next > < Previous

Related Solutions

Applications of higher order differential equations A spring has one of its ends fixed, and a...
Applications of higher order differential equations A spring has one of its ends fixed, and a force of 15 N stretches it 20cm. A mass of 4 Kg is attached to the end of the spring, and the system is set in motion with initial position = 60 cm and initial velocity = 1.5 m/s. (a) Find the spring constant. (b) Write a problem of initial conditions for spring stretching, in meters. (c) Solve the problem posed in (b). (d)...
3) Laplace Transform and Solving first order Linear Differential Equations with Applications The Laplace transform of...
3) Laplace Transform and Solving first order Linear Differential Equations with Applications The Laplace transform of a function, transform of a derivative, transform of the second derivative, transform of an integral, table of Laplace transform for simple functions, the inverse Laplace transform, solving first order linear differential equations by the Laplace transform Applications: a)))))) Series RL circuit with ac source [electronics]
4) Laplace Transform and Solving second order Linear Differential Equations with Applications The Laplace transform of...
4) Laplace Transform and Solving second order Linear Differential Equations with Applications The Laplace transform of a function, transform of a derivative, transform of the second derivative, transform of an integral, table of Laplace transform for simple functions, the inverse Laplace transform, solving first order linear differential equations by the Laplace transform Applications: a) Series RLC circuit with dc source b) Damped motion of an object in a fluid [mechanical, electromechanical] c) Forced Oscillations [mechanical, electromechanical] You should build the...
Report about (Applications of Differential Equations in Heat Exchanger System)
Report about (Applications of Differential Equations in Heat Exchanger System) 
Write the second order differential equation as a system of two linear differential equations then solve...
Write the second order differential equation as a system of two linear differential equations then solve it. y" + y' - 6y = e^-3t y(0) =0   y'(0)=0
Differential Equations. A 10kg weight is attached to a wall horizontally via a spring. The rest...
Differential Equations. A 10kg weight is attached to a wall horizontally via a spring. The rest (equilibrium) length of the spring is 0.2m. The spring has stiffness coefficient k = 50. The weight drags along the ground, giving an effective damping coefficient of b = 40. We will ignore gravity and all other outside forces on the spring. If the weight is pulled to a position 0.5m away from the wall (thus +0.3m past equilibrium) and then flicked toward the...
Topic: Differential Equations; reduction order. The indicated fuction y1(x) is a solution of the given differential...
Topic: Differential Equations; reduction order. The indicated fuction y1(x) is a solution of the given differential equation. Use the reduction order technique to find a second solution y2(x). xy'' + y' = 0;    y1= ln(x) Please, explain deeply each part of the solution, and include complete algebraic explanation as well. Otherwise, the answer will be negatively replied.
Solve two different first order differential equations (one linear and one non-linear) both analytically and numerically...
Solve two different first order differential equations (one linear and one non-linear) both analytically and numerically and compare the results in tabular and graphical forms. Include at least two different numerical solution techniques for each differential equation analyzed.
DIFFERENTIAL EQUATIONS: 1. A body with a weight of 3.5 grams force hangs from a spring...
DIFFERENTIAL EQUATIONS: 1. A body with a weight of 3.5 grams force hangs from a spring stretching it 3.21 centimeters. Initially the body starts from rest 3.4 centimeters below its equilibrium position. The medium in which the body moves offers a resistance force to movement that is numerically equal to 1/8 of its instantaneous speed. Knowing that there is an external force, changing in time, which is defined by the formula: f (t) = 7cos (t) grams force. Find the...
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...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT