Question

In: Physics

A particle of mass m = 1 oscillates without friction attached to a spring with k...

A particle of mass m = 1 oscillates without friction attached to a spring with k = 4. The motion of the particle is driven by the external force F(t) = 3 t cos(t). Find the equation of motion and solve it. Discuss the physical meaning of the solution.

Solutions

Expert Solution


Related Solutions

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 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 mass of 1.1kg is attached to a spring and constrained to move without friction along...
A mass of 1.1kg is attached to a spring and constrained to move without friction along the x-axis. The mass is attached to a spring of spring constant 80?? N m ; one end of the spring is attached to a fixed point along the x-axis while the other is attached to the mass. The equilibrium position of the mass is the origin. The mass has a position as a function of time which can be expressed: ?(?)=?cos(??+?) x (...
Consider a mass spring system. The spring has a constant k=30N/m and mass=3kg. The mass oscillates...
Consider a mass spring system. The spring has a constant k=30N/m and mass=3kg. The mass oscillates w/amplitude of 10cm. a.)what is the frequency of oscillation b.) what is the displacement at time t=0 c.) when is the first time the mass is at maximum displacement? (t=?) d.) what is the maximum acceleration felt by the mass? Where in the motion does this occur? e.)what is the minimum acceleration felt by the mass? Where in the motion does this occur? f.)What...
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 attached to a spring oscillates with a period of 3.15 s. (a) If the...
A mass attached to a spring oscillates with a period of 3.15 s. (a) If the mass starts from rest at x = 0.0480 m and time t = 0, where is it at time t = 6.97 s? m? (b) Is the mass moving in the positive or negative x direction at t = 6.97 s? positive x direction? negative x direction?
A 0.900-kg block attached to a spring with force constant k = 1.20 N/m oscillates with...
A 0.900-kg block attached to a spring with force constant k = 1.20 N/m oscillates with an amplitude equal to half its natural length. The natural (un-stretched) length of the spring is 18.0 cm. (a) When submitting your work, sketch the figure below illustrating the position, and directly underneath that, the velocity of the mass as a function of time. Assume that x = 9.00 cm and v =0 m/s when t = 0.00 s. Label the amplitude A and...
A 0.770-kg mass attached to a vertical spring of force constant 147 N/m oscillates with a...
A 0.770-kg mass attached to a vertical spring of force constant 147 N/m oscillates with a maximum speed of 0.322 m/s. Calculate the period related to the motion of the mass. Calculate the amplitude. Calculate the maximum magnitude of the acceleration.
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...
10. It has a mass m attached to a spring of elastic constant k and that...
10. It has a mass m attached to a spring of elastic constant k and that suffers a damping b proportional to the speed, being b = k / 2. If the initial amplitude is A: a) How long does it take until the amplitude is worth A / 2? b) How long does it take until half of the initial energy has dissipated?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT