2. (UC-3) A mass weighing 64 pounds stretches a spring 3.2 feet. The mass is initiallyreleased from rest from a point 4 feet below the equilibrium position, and the subsequentmotion takes place in a medium that offers a damping force that is numerically equal to8 times the instantaneous velocity.Use the method of undetermined coefficients to find the equation of motion if the massis driven by an external force equal to f(t) = 37 cos(3t).

Newton's 2nd law of motion for the system is, md2xdt2=-kx-βdxdt+ftd2xdt2+kmx+βmdxdt=ftm Now,…

Answered: 2. (UC-3) A mass weighing 64 pounds…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

100%

2. (UC-3) A mass weighing 64 pounds stretches a spring 3.2 feet. The mass is initially
released from rest from a point 4 feet below the equilibrium position, and the subsequent
motion takes place in a medium that offers a damping force that is numerically equal to
8 times the instantaneous velocity.
Use the method of undetermined coefficients to find the equation of motion if the mass
is driven by an external force equal to f(t) = 37 cos(3t).

Expert Solution

Step 1

Newton's 2nd law of motion for the system is,

$\begin{array}{rcl} m \frac{d^{2} x}{d t^{2}} & = & - k x - β \frac{d x}{d t} + f (t) \\ \frac{d^{2} x}{d t^{2}} + \frac{k}{m} x + \frac{β}{m} \frac{d x}{d t} & = & \frac{f (t)}{m} \end{array}$

Now, consider the given data and put the values into the above equation,

$g = 32 \frac{ft}{s^{2}}, β = 8, m = 2 slug, and k = 20 \frac{lb}{ft}$

So, we get,

$\begin{array}{rcl} \frac{d^{2} x}{d t^{2}} + \frac{20}{2} x + \frac{8}{2} \frac{d x}{d t} & = & \frac{37 \cos (3 t)}{2} \\ \frac{d^{2} x}{d t^{2}} + 4 \frac{d x}{d t} + 10 x & = & 18.5 \cos (3 t) \end{array}$