This problem is an example of critically damped harmonic motion.

This problem is an example of critically damped harmonic motion. A mass m=6kg is attached to both a spring with spring constant k=96N/m and a dash-pot with damping constant c=48N⋅s/m . The ball is started in motion with initial position x0=5m and initial velocity v0=−24m/s . Determine the position function x(t) in meters. x(t)= Graph the function x(t) . Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected ( so c=0 ). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t)=C0cos(ω0t−α0). Determine C0, ω0 and α0. C0= ω0= α0= (assume 0≤α0<2π ) Finally, graph both function x(t) and u(t) in the same window to illustrate the effect of damping.

Expert Solution

Colby Messinger answered 2 years ago

This problem is an example of over-damped harmonic motion. A mass m=4kg is attached to both...

This problem is an example of over-damped harmonic motion. A mass m=4kg is attached to both a spring with spring constant k=72N/m and a dash-pot with damping constant c=36N⋅s/m The ball is started in motion with initial position x0=−3m and initial velocity v0=4m/s Determine the position function x(t) in meters.

(a)Use Netwons Second Law of Motion to prove that the equation governing the forced damped harmonic...

(a)Use Netwons Second Law of Motion to prove that the equation governing the forced damped harmonic oscillator (spring-mass system) is: mx"(t) + cx'(t) + kx(t) = F(t): (Explain what the constants m; c; k are and what the function F(t) is. Draw a picture of the system.) (b)Assume m = 1; c = 0; k = 4; that F(t) = cos(2t); and that the object attached to the spring begins from the rest position. Find the position function using the...

Please provide an example of a damped harmonic oscillator. They are more common than undamped or...

Please provide an example of a damped harmonic oscillator. They are more common than undamped or simple harmonic oscillators. What do you think there is any harmonic motion in the physical world that is not damped harmonic motion? Try to make a list of five examples of undamped harmonic motion and damped harmonic motion. Which list was easier to make? Why are the group of the peoples in general ordered to “route step” (walk out of step) across a bridge?

Mechanical vibration. Examples of forced damped oscillation with harmonic force.

particle is in simple harmonic motion along the x axis. The amplitude of the motion is...

particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = −1 2x1, the kinetic and potential energies are: A. K = 5 J and U = 3J B. K = 5 J and U...

The motion of a forced damped spring system is: ?(?) = 2 sin 4? + ?...

The motion of a forced damped spring system is: ?(?) = 2 sin 4? + ? ^-? cos 6?. A) What is the driving frequency? B) What is the transient part? C) What is the steady-periodic part? Could someone provide explanations as to how to obtain these solutions as I am lost?

can someone tell me the differences between “Free Undamped Motion”, “Free Damped Motion”, “Driven Undamped Motion”,...

can someone tell me the differences between “Free Undamped Motion”, “Free Damped Motion”, “Driven Undamped Motion”, or “Driven Damped Motion” sample drawings will be helpful.

Write a discussion and conclusion for simple harmonic motion.

Problem 1. A mass oscillates on a horizontal spring performing a simple harmonic motion. Time t...

Problem 1. A mass oscillates on a horizontal spring performing a simple harmonic motion. Time t = 0.00 sec corresponds to the moment when the mass is at the location 15.0 cm to the left of the equilibrium, and moving to the right. 1. If the maximal speed of this oscillator is 1.50 m/s, and the maximal magnitude of its acceleration is 4.50 m/s2 what is the amplitude and the period of this oscillator? 2. Using circle of reference, calculate...

1.For a damped simple harmonic oscillator, the block has a mass of 2.3 kg and the...

1.For a damped simple harmonic oscillator, the block has a mass of 2.3 kg and the spring constant is 6.6 N/m. The damping force is given by -b(dx/dt), where b = 220 g/s. The block is pulled down 12.4 cm and released. (a) Calculate the time required for the amplitude of the resulting oscillations to fall to 1/8 of its initial value. (b) How many oscillations are made by the block in this time? 2.An oscillator consists of a block...

Question