A 1kg mass is attached to a spring immersed in a fluid that exerts a dampingforce...

A 1kg mass is attached to a spring immersed in a fluid that exerts a dampingforce of 5N per 2m/s. When the spring is extended 0.5m beyond equilibrium,a force of 2N is exerted by the spring. Assume the mass is returned to rest.Find the equation for the position of the mass relative to equilibrium in theevent that the following driving forces are applied. One, an impulse of 1Nafter 0.5s. Two, a force of sin(π2t)N applied for a duration of 1s starting at1s.

Also, if the formula for impulse is written as my" + γy' + ky = impulse function.

Please explain how to calculate γ here.

Expert Solution

genius_generous answered 2 years ago

a crate of stuffed kittens with a mass of 1kg compresses a spring a distance of...

a crate of stuffed kittens with a mass of 1kg compresses a spring a distance of 2.84m. The spring has a spring constant of 250N/m. The crate is released and slides across a rough surface with a kinetic friction coefficient of 0.38 for a distance of 62m before colliding with and sticking to another crate. The second crate is filled with cans of smoked turkey and has a mass of 2kg. The two crates then slide horizontally off a vertical...

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 particle of mass m is attached to a spring with a spring constant k. The...

A particle of mass m is attached to a spring with a spring constant k. The other end of the spring is forced to move in a circle in the x ? y plane of radius R and angular frequency ?. The particle itself can move in all 3 directions. Write down the Lagrangian, and derive the equations of motion.

A block with a mass M is attached to a horizontal spring with a spring constant...

A block with a mass M is attached to a horizontal spring with a spring constant k. Then attached to this block is a pendulum with a very light string holding a mass m attached to it. What are the two equations of motion? (b) What would these equations be if we assumed small x and φ? (Do note that these equations will turn out a little messy, and in fact, the two equations involve both variables (i.e. they are...

A block with a mass of 0.488 kg is attached to a spring of spring constant...

A block with a mass of 0.488 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What is the amplitude of the oscillation? A block with a mass of 0.976 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What...

A spring is stretched by 7in by a mass weighing 15lb. The mass is attached to...

A spring is stretched by 7in by a mass weighing 15lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.1lb⋅s/ft and is acted on by an external force of 5cos(9t)lb. Determine the steady state response of this system. Use 32ft/s2 as the acceleration due to gravity. Pay close attention to the units.

You are bringing a spring pendulum (i.e. a mass attached to a spring) and a regular...

You are bringing a spring pendulum (i.e. a mass attached to a spring) and a regular pendulum (think ball on a string) to the International Space Station. Because the ISS is in orbit around the Earth you (and everything else on board) experience apparent weightlessness. Under these conditions, which of the following statements is correct when you displace both pendulums from their respective equilibrium positions (ie try to make them oscillate): Group of answer choices The spring pendulum will oscillate....

1. A 1 kilogram mass is attached to a spring with a spring constant of 4...

1. A 1 kilogram mass is attached to a spring with a spring constant of 4 N/m. Write the equation of motion if the spring is stretched 25 cm below the equilibrium position and released. a) Suppose the system experiences a constant forcing function downwards of 4 N. (Note that one would need to divide by the mass, but the mass is 1 kg so we don’t see a difference here.) Solve the non-homogeneous equation. (Keep everything else about the...

A block of mass m = 2.5 kg is attached to a spring with spring constant...

A block of mass m = 2.5 kg is attached to a spring with spring constant k = 640 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 27° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.11. In the initial position, where the spring is compressed by a distance of d = 0.19 m, the mass is at...

A block of mass m = 2.6kg is attached to a single spring of spring constant...

A block of mass m = 2.6kg is attached to a single spring of spring constant k = 4.4Nmand allowed to oscillate on a horizontal, frictionless surface while restricted to move in the x-direction. The equilibrium position of the block is x=0m. At time t=0s the mass is at position x=2.7m and moving with x-component of velocity vx=−6.8ms. What is the x-component of velocity at time t=1.3s? Answer in meters per second.

Question