Suppose a spring with spring constant 2 N/m is horizontal and has one end attach

Question

Suppose a spring with spring constant 2 N/m is horizontal and has one end attached to a wall and the other end attached to a 3 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 3 Ns/m3

A) Set up a differential equation that describes this system. Let xx to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x,x,x. Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium.

I got 3x''+3x'+2x=0.

B)Find the general solution to your differential equation from the previous part. Use c1 and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c1 as c1 and c2 as c2. Your answer should be an equation of the form x=…

I got x=c1e(-.5t)cos((sqrt(15)/6)t)+c2e(-.5t)sin((sqrt(15)/6)t).

C)Is this system under damped, over damped, or critically damped? Enter a value for the damping constant that would make the system critically damped.

I found that it is underdamped but I can't figure out what value will make it critically damped.

Thank You!!

Explanation / Answer

Compare the equationn with mx'' + cx' + kx =0

here, m =3, c=3, k=2

to find damping, calculate c2 -4mk = 9-24= -15

So it is underdamped,

For critically daped, c2 -4mk =0

c2=4mk

c= 2(mk) = 2*(3*2) =26 = 4.899

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.