A mass of 1 slug is placed on a vertical spring with constant k = 16...

A mass of 1 slug is placed on a vertical spring with constant k = 16 lb/ft. Starting at t = 0 a force equal to f(t)= 8sin(4t) is applied to the system. Find the equation of motion if the surrounding system offers a damping force equal to 8 times the instantaneous speed. Consider x(0)=0 x'(0)=0.   differential equations

Expert Solution

milcah answered 2 years ago

A mass of 1 kg is attached to a spring with constant k = 16 kg/ft....

A mass of 1 kg is attached to a spring with constant k = 16 kg/ft. Initially at equilibrium, a periodic external force of f(t) = cos(3t) begins to affect the mass for t > 0. Find the resultant motion x(t).

A box of mass 1kg is placed on a vertical spring (k=1000N/m) and pushed down so...

A box of mass 1kg is placed on a vertical spring (k=1000N/m) and pushed down so that the spring is compressed by 0.3m from the unstretched length. When the spring is released, what is the maximum height above the initial position (when the spring is compressed) the box rises?

1. A vertical spring has a spring constant of 2500 N/m. A ball with a mass...

1. A vertical spring has a spring constant of 2500 N/m. A ball with a mass of 0.25 kg is on top of the spring. Use energy conservation to answer the following questions. Sketch the situation for each part. A. If the spring is compressed 8.3 cm how much energy is stored in the spring? B. When you release the spring, it pushes the ball upward. What is the speed of the ball at the instant it leaves the spring?...

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.

1. A block of mass m attached to a spring with spring constant k oscillates horizontally...

1. A block of mass m attached to a spring with spring constant k oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5 cm. Taking m = 100 gm, and spring constant = 2.5 N/m, a) Find out the equations of position, velocity, and acceleration of the ball. Find also the total energy of the block when its velocity was 20 cm/s. b) Oscillating particles generate waves. What will be the equation of a...

A mass suspended at the end of a light Spring and spring constant K is set...

A mass suspended at the end of a light Spring and spring constant K is set into vertical motion use lagrange's equation to find the equation of motion of the mass

A mass m = 1 kg is attached to a spring with constant k = 4...

A mass m = 1 kg is attached to a spring with constant k = 4 N/m and a dashpot with variable damping coefficient c. If the mass is to be pulled 5 m beyond its equilibrium (stretching the spring) and released with zero velocity, what value of c ensures that the mass will pass through the equilibrium position and compress the spring exactly 1 m before reversing direction? c =

A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is...

A mass of 1 slug, when attached to a spring, stretches it 2 feet. It is released from a point 1 foot above the equilibrium position with a downward velocity of 2 ft/s. 1) Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 4 times the instantaneous velocity. 2) Classify the motion as underdamped, overdamped, or critically damped.

A mass of 1 slug, when attached to a spring, stretches it 2 feet and then...

A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = 10 sin(4t) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(t) = ____________ft

A 20.0-g object is placed against the free end of a spring (with spring constant k...

A 20.0-g object is placed against the free end of a spring (with spring constant k equal to 25.0 N/m) that is compressed 10.0 cm. Once released, the object slides 1.25 m across the tabletop and eventually lands 0.61 m from the edge of the table on the floor, as shown in the figure. Calculate the coefficient of friction between the table and the object. The sliding distance includes the compression of the spring and the tabletop is 1.00 m...

Question