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 between the mass and the equilibrium point t seconds after motion starts.

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

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...

undamped spring-mass system with mass 6 kg and a spring which is stretched 2 meter by...

undamped spring-mass system with mass 6 kg and a spring which is stretched 2 meter by 10 Newtons. Suppose an oscillating force 3 cos(ωt) is acting on the system. What value of ω causes resonance? For this value of ω, find a formula for x, the distance between the weight and equilibrium t seconds after the weight starts at x = 0 at rest.

A spring with a 6-kg mass and a damping constant 5 can be stretched 1.5 meters...

A spring with a 6-kg mass and a damping constant 5 can be stretched 1.5 meters beyond its natural length and held at rest there by a force of 7.5 newtons. Suppose the spring is stretched 3 meters below spring-mass equilibrium and then released with zero velocity. Find the position of the mass after t seconds. y(t)=? Please show all the work.

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).

An object with m1 = 5kg is attached to a spring of negligible mass. This mass/spring...

An object with m1 = 5kg is attached to a spring of negligible mass. This mass/spring combination is then slid horizontally on a frictionless surface with a velocity of 5m/s towards a stationary object with m2 = 6kg. Upon impact, the spring compresses, then we examine two cases. First, find the velocities of the two objects assuming the spring completely relaxes again after the interaction. Second, assume that m2, after they separate, slides up a frictionless incline. (a) What is...

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 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...

7) A spring has is stretched horizontally to the right from a wall 0.5 meters by...

7) A spring has is stretched horizontally to the right from a wall 0.5 meters by a force of 40 newtons. This spring has a mass of 10 kg. The mass is pulled to the right (from the equilibrium position) 1 meter and released (at t = 0) with an initial velocity to the right of 2 meters per second. I) Write down the differential equation that governs the motion of the mass. Include the initial conditions. (assume no damping)....

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 spring with a 4-kg mass and a damping constant 3 can be held stretched 1...

A spring with a 4-kg mass and a damping constant 3 can be held stretched 1 meters beyond its natural length by a force of 4 newtons. Suppose the spring is stretched 2 meters beyond its natural length and then released with zero velocity, In the notation of the text, what is the value ?2−4??c2−4mk? m2kg2/sec2m2kg2/sec2 Find the position of the mass, in meters, after t seconds. Your answer should be a function of the variable t with the general form...

Subjects