If you look at the rest of the solution, I don't see where they treat things the way you imply they're doing. Yet, they magically come up with the correct formula in the end. And even even if what you say were true, that doesn't do anything to explain the rest of the problems with their...
Please open the attached file in which I have outlined the solution given in the Instructor's Solutions Manual. I have also noted in the document where I believe the errors occur.
I'm so sorry. I'm an expert in LaTex, but I'm a novice when it comes to MathJax, and I'm having a lot of trouble posting it. What I'm going to do is to write it up in Latex and post it as an attachment. Please be patient.
The statement of the problem is:
Consider a taut string that has a mass per unit length ##\mu_1## carrying transverse wave pulses of the form ##y = f(x - v_1 t)## that are incident upon a point P where the string connects to a second string with mass per unit length ##\mu_2##.
Derive $$1 = r^2...
Yes, I got the same result. I fully agree with your analysis that if you only consider the steady-state solution, going as fast as possible should minimize the amplitude of the vibrations. As I said in my original post, driving at a velocity that would shift the driving force towards the...
Shock absorbers in an automobile are typically critically damped according to the natural frequency of the suspension springs in the automobile suspension. So while I agree that the bumps in the road play the part of a driving force, I don't think that changes the situation.
We know the "damped frequency" by the fact that the system is critically damped, in which case, ω=0.
I don't know that diddling around to arrive at some value that has the correct units is a valid method to solve a physics problem. It may be a guide that your answer isn't invalid, but it...
First of all, the problem is not clearly defined as they don't specify if the given mass is the total mass of the car, or just the sprung mass of the car, which is really what's relevant. In any case, with the limited information given, it seems like one is forced to make the assumption that...
Consider a conical pendulum like that shown in the figure. A ball of mass, m, attached to a string of length, L, is rotating in a circle of radius, r, with angular velocity, ω. The faster we spin the ball (i.e., the greater the ω), the greater the angle, θ, will be, and thus, the smaller the...