A 3-kg mass is attached to the end of a coil spring with stiffness k=48N/m ....

A 3-kg mass is attached to the end of a coil spring with stiffness k=48N/m . The mass is then pulled down 0.5m (from its equilibrium position) and released at t = 0 with an initial velocity of 2 m/sec directed upward. Neglect the resistance of the medium. a) Determine the resulting displacement and velocity as functions of time. b) Find amplitude, period and frequency of the motion. c) At what time does the weight first pass through the equilibrium position?

Solutions

Expert Solution

samet mamat answered 2 months ago

Next > < Previous

Related Solutions

An object with mass 3.5 kg is attached to a spring with spring stiffness constant k...

An object with mass 3.5 kg is attached to a spring with spring stiffness constant k = 270 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s.(a) Calculate the amplitude of the motion._____ m(b) Calculate the maximum velocity attained by the object. [Hint: Use conservation of energy.]______ m/s

A 1 3 -kg mass is attached to a spring with stiffness 4 N/m. The damping...

A 1 3 -kg mass is attached to a spring with stiffness 4 N/m. The damping constant for the system is 2 N-sec/m. The mass is displaced 1 2m to the left and given an initial velocity of 2 m/s to the right. (a) Determine the equation of the motion of mass and express it in the form A e αt sin(βt + φ) by finding the constants A, α, β and φ in radians. (b) Find the time t...

A mass m = 3.27 kg is attached to a spring of force constant k =...

A mass m = 3.27 kg is attached to a spring of force constant k = 60.9 N/m and set into oscillation on a horizontal frictionless surface by stretching it an amount A = 0.17 m from its equilibrium position and then releasing it. The figure below shows the oscillating mass and the particle on the associated reference circle at some time after its release. The reference circle has a radius A, and the particle traveling on the reference circle...

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 block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m...

a block of mass m=0.10 kg attached to a spring whose spring constant is k=2.5 N/m . At t=0.2s, the displacement x=-0.3m, and the velocity v=-2.0m/s a) find the equation of displacement as a function of time b) sketch the displacement as a function of time for the first cycle starting t=0s

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 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 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 block with mass 5 kg is attached to the end of a horizontal spring with...

A block with mass 5 kg is attached to the end of a horizontal spring with spring constant 200N/m. The other end of the spring is attached to a wall. The spring is stretched 10cm in the positive directions from its equilibrium length. Assume that the block is resting on a frictionless surface. A) When the spring is fully stretched, what is the magnitude of the force from the spring on the block? B) We then release the block, letting...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it...

A 8.50 kg mass is attached to the end of a hanging spring and stretches it 28.0 cm. It is then pulled down an additional 12.0 cm and then let go. What is the maximum acceleration of the mass? At what position does this occur? What is the position and velocity of the mass 0.63 s after release?

Subjects