The hollow cylinder from the last problem is attached to a spring with spring constant k...

The hollow cylinder from the last problem is attached to a spring with spring constant k = -1.6 and extended to an initial displacement of 9 cm

A) What is the period if it takes 20 s to travel to a point halfway between the 1st equilibrium point and the negative extreme displacement?

B) What is the displacement 7 s later?

C) What is the velocity at this point?

D) What is the acceleration?

Expert Solution

genius_generous answered 7 months ago

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.

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

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 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 =

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?

A mass m=4 is attached to both a spring with spring constant k=145 and a dash-pot...

A mass m=4 is attached to both a spring with spring constant k=145 and a dash-pot with damping constant c=4. The ball is started in motion with initial position x0=1 and initial velocity v0=6 . Determine the position function x(t) . x(t)=? Note that, in this problem, the motion of the spring is underdamped, therefore the solution can be written in the form x(t)=c1e^(-ρt)cos(ω1t-α1) . Determine c1, ω1, ρ and α1. c1=? ω1=? ρ=? α1=? Graph the function x(t) together...

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 spring with force constant k = 175 N/m is attached to the ground. On top...

A spring with force constant k = 175 N/m is attached to the ground. On top of the spring a 1.30 kg metal pan is attached. The combination could be used as a scale, but we are going to do something more interesting. We place a metal ball with mass 0.250 kg on the tray and then the tray is pushed down 0.150 m below its equilibrium point and released from rest (take this as t = 0). a) At...

A hollow sphere, a solid cylinder, and a hollow cylinder are all released from rest at...

A hollow sphere, a solid cylinder, and a hollow cylinder are all released from rest at the top of a ramp. Which object reaches the bottom of the ramp first? (a) The hollow sphere (b) The solid cylinder (c) The hollow cylinder (d) They all reach the bottom of the ramp at the same time A hollow sphere, a solid cylinder, and a hollow cylinder are all released from rest at the top of a ramp. Which object has the...

Question