Question

Please help solve this, using the equation m(\frac{d^{2}y}{dt^{2}}) + b(\frac{dy}{dt}) + ky = 0 to get through the problem.

When an object of mass 5kg is hanged from a string, the string stretches by 0.5m. We suppose that the damping force of the st

Additional information:

m(\frac{d^{2}y}{dt^{2}}) + b(\frac{dy}{dt}) + ky = 0 where the initial position y_{0} = y(0) , the initial speed v_{0} = v(0) = y'(0)

The above differential equation can also be written as:

(mD^{2} + bD + k)y = 0

If b^{2} - 4km < 0 , there is light damping where the solution has the form ( where r and w are two positive constants)

y(t) = Ae^{-rt} sin(wt + \phi ) or y(t) = e^{-rt}(C_{1} sin(wt) + C_{2} cos(wt))

If b^{2}-4km > 0, there is heavy damping where,

y(t) = C_{1}e^{-r_{1}t} + C_{2}e^{-r_{2}t} where r_{1} and r_{2} are two positive constants

If b^{2}- 4km = 0, there is critical damping where,

y(t) = (C_{1}+C_{2}t)e^{-rt} where r is a positive constant

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Doubt in this then comment below.. i will help you..

.

please thumbs up for this solution..thanks..

.

mas, Ele os s * + to xf Goa = 1 Toucos(64) + en + 12 * = 340 cose 6 ty 21 & Polo a ro) ot 2D+ 1200 Shu ☺ Da ( 340 Cos (6+1) 2

20- ܩܐ 10 20-

bul 39 ceslji t) + 68 sin 3 JT + 127 sinlot) 39 ccs(66) 3 Xitro t= 0.386 18508 below us equillibran 2 Amplitude (43) 17 5 ㅋ 3

Add a comment
Know the answer?
Add Answer to:
Please help solve this, using the equation to get through the problem. Additional information: where the...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x,...

    a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x, t) = Acos(kx − t) where A, k, are positive constants. 2. h(x, t) = Ae where A, k, are positive constants. 3. p(x, t) = Asinh(kx − t) where A, k, are positive constants. 4. q(x, t) = Ae where A, a, are positive constants. 5. An arbitrary function: f(x, t) = f(kx−t) where k and are positive constants. (Hint: Be careful with...

  • DIFFERENTIAL EQUATION PROBLEM An object with a mass of 2 kg moves along the x-axis and...

    DIFFERENTIAL EQUATION PROBLEM An object with a mass of 2 kg moves along the x-axis and we will assume that the positive direction of movement is to the right. Only one force (in N) is present and opposes the movement. Let be the speed of the object (in m / s) at time t. The object starts from the origin (x = 0) with an initial speed of 75 m / s. Suppose that the resistance force has a magnitude...

  • Solve the following wave partial differential equation of the vibration of string for ?(? ,?). yxx=16ytt...

    Solve the following wave partial differential equation of the vibration of string for ?(? ,?). yxx=16ytt y(0,t)=y(1,t)=0 y(x,0)=2sin(x)+5sin(3x) yt(x,0)=6sin(4x)+10sin(8x) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

  • Relativistic case: Starting from equation invert it to get . Restore factors of G and c. Get the...

    Relativistic case: Starting from equation invert it to get . Restore factors of G and c. Get the expression for V(r), the "coordinate speed," for a particle falling from rest at . Take the Derivative with respect to r to find the location where the maximum coordinate speed occurs. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

  • Can I get a solution for this question? It's quite hard to solve. There is no reference about and I don't get w...

    Can I get a solution for this question? It's quite hard to solve. There is no reference about and I don't get what this question's purpose is. Is alpha the alpha from bernoulli's equation? Question: An approximate equation for the velocity distribution in a pipe with turbulent flow is where Vmax is the centerline velocity, is the distance from the wall of the pipe, r is the radius of the pipe, and n is an exponent that depends on the...

  • COMPLEX ANALYSIS: Solve the integral where and . Please use JORDAN'S LEMMA and show all of...

    COMPLEX ANALYSIS: Solve the integral where and . Please use JORDAN'S LEMMA and show all of your work. Thank you! We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

  • (A) Find the largest x-interval where the initial value problem has a unique solution: Where A,...

    (A) Find the largest x-interval where the initial value problem has a unique solution: Where A, B, C, D, E, F are some known constants. (B) Determine whether the set of functions could form a fundamental set of solution of a linear differential equation Thank you We were unable to transcribe this image5, sinx, cos2.c

  • d.) using the graph's slope - 32.7 - and the equation of the slope (where L...

    d.) using the graph's slope - 32.7 - and the equation of the slope (where L (length of string) = 1 meter) determine the value of and compare it to the given value which is 4.4g/m. (I think I'm doing something wrong with the units because I'm getting over 50% error?) e.) Why is there a difference between the two numbers? We were unable to transcribe this imageWe were unable to transcribe this imageMass (kg) sqrroot(m*g) (N) f (Hz) 18...

  • Consider the differential equation for , which models a population of fish with harvesting that...

    Consider the differential equation for , which models a population of fish with harvesting that is governed by the logistic equation and a number of fish H caught and removed every unit of time (harvesting). Here the parameters r, K, and H are all positive. a) Assume that . Draw the phase plane. b) Assume that . What happens to the population of fish as t increases? Can I have a step-by-step walkthrough on how to solve these two. I...

  • Applying Newton's 2nd law, Fnet=ma, then to this system, along the direction of motion (parallel...

    Applying Newton's 2nd law, Fnet=ma, then to this system, along the direction of motion (parallel to the swinging bob), we find −mgsin⁡θ=ma. (Note, the negative sign is required since the acceleration in our picture, which is to the right at this moment, is opposite to the angular displacement from the vertical, which is to the left.) This equation is extremely difficult to solve, so let us simplify it by assuming that the pendulum's swings only through a very small angle,...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT