In a spring-mass-dashpot system, a force of 1 Newtons is required to stretch the spring for...

In a spring-mass-dashpot system, a force of 1 Newtons is required to stretch the spring for .05 meters. A mass of 4 kg is hung from the spring and also attached to a viscous damper that has a damping constant 8 Newton-sec/m. The mass is suddenly set in motion from its equilibrium location at t = 0 by an external force of 8 cost Newtons with initial velocity 0 m/sec. Find the transient solution and the steady state solution of the system.

Expert Solution

Colby Messinger answered 1 month ago

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...

Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 6 meters by a...

Consider a mass-spring-dashpot system with mass 5kg, a spring which is stretched 6 meters by a force of 20N, and a dashpot which provides 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 between the mass...

A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that...

A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that imparts a damping force equal to 14 times the instantaneous velocity of the mass. Find the equation of motion if the mass is released from equilibrium with an upward velocity of 3 m/sec. SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS) SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS) SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS) SOLVE THIS USING MATLAB...

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 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)...

Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant c...

Suppose that the mass in a mass-spring-dashpot system with m = 10, the damping constant c = 9, and the spring constant k = 2 is set in motion with x(0) = -1/2 and x'(0) = -1/4. (a) Find the position function x(t). (b) Determine whether the mass passes through its equilibrium position. Sketch the graph of x(t).

A particle of mass 1 is attached to a spring dashpot mechanism. The stiffness constant of...

A particle of mass 1 is attached to a spring dashpot mechanism. The stiffness constant of the spring is 3 N/m and the drag force exerted on the particle by the dashpot mechanism is 4 times its velocity. At time t=0, the particle is stretched 1/4 m from its equilibrium position. At time t=3 seconds, an impulsive force of very short duration is applied to the system. This force imparts an impulse of 2 N*s to the particle. Find the...

A mass-spring-dashpot system is described by my′′ + cy′ + ky = Fo cos ωt, see...

A mass-spring-dashpot system is described by my′′ + cy′ + ky = Fo cos ωt, see §3.6 Eq. (17). This second-order differential equation has been used in simulations, such as this one at the PhET site: https://phet.colorado.edu/en/simulation/legacy/resonance. For m = 2.53kg, c = 0.502N/(m/s), k = 97.2N/m, Fo = 97.2×0.5N = 48.6N,and ω = 2.6, the equation becomes 2.53y′′ + 0.502y′ + 97.2y = 48.6 cos(ωt) ....................... (1) (a) Given the initial value y(0) = 2.20, y′(0) = 0, solve...

1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring...

1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring with a stiffness of 9. The damping constant is 6. Derive the function (1) that determines the distance from the equilibrium point if the initial position is 3 meters from the equilibrium point and the initial speed is 3 meters per second. a.) What is the maximum distance from the equilibrium point? b.) Determine the general solution of the nonhomogeneous linear differential equation using...

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.

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