Subscribe to:
Post Comments (Atom)
skip to main |
skip to sidebar
Fall 2008 -- Purdue University -- West Lafayette, IN
Blog Post LABELS
- Blog Challenge Questions (9)
- Chapter 2 (2)
- Chapter 3 (19)
- Chapter 5 (11)
- Chapter 6 (23)
- Chapter 7 (7)
- Chapter 8 (9)
- Exam 1 (5)
- Exam 2 (4)
- Exam 3 (17)
- Exams (2)
- Final Exam (7)
- General (6)
- Gravity (2)
- Homework (2)
- in class (1)
- Lectures (1)
- Quizzes (2)
- Spring 2008 Archive (87)
- Spring-Mass Simulator (1)
- Student-Generated Solutions (1)
- Summer 2008 Archive (72)
13 comments:
As you have stated, the free response for the system is given by: x(t)= C cos(omega_n*t) + S sin(omega_n*t) where C and S are found from enforcing the IC's. From this, the maximum amplitude of response is x_max = sqrt(C^2 + S^2).
There is an infinite number of IC's that can produce the same value of x_max. I suggest using something simple, such as an initial displacement x(0) and from rest, x_dot(0) = 0. Use this to solve for x_max in terms of the parameters of the problem.
Let us know if this does not help.
That makes sense, however I just keep thinking it will be zero, because c will be zero if x(0) = 0 and s will be zero if xdot(0) = 0.
I think that x(o) is equal to our initial displacement (assuming that we move the disk from equilibrium) and therefore C is not equal to zero, but instead this distance. If I'm thinking right, this also turns out to be the maximum amplitude that we're solving for.
In example problem on pg. 15 in our notes, we used (k/m)^.5 to find w_n. For this problem, do we use k or .5k to calculate w_n?
you should just use k and not .5k. What affect does the friction force have on the problem if any?
How can we calculate x(0) and x_dot(0)?
Brian,
To solve for wn, you must use the newton/Euler equations and kinematics to establish an EOM. When you have your EOM, you can plug in the correct coefficients of k and m into your (k/m)^.5 equation.
To calculate x(t). In it's initial condition of t=0 it is in a relaxed position. x(t) = cCos(wn*t) + sSin(wn*t) = 0. Therefore, C must = 0. The constant "s", aka "xo" cannot be determined because of the initial conditions. Now that you have the equation for x(t), you can take the derivatives to solve for xdot and xdoubledot. I hope this helps.
To elaborate even more on Byron's comment, at t=0, and when x(t) = cCos(wn*t) + sSin(wn*t) = 0, you know that sin(0) = 0 so what you have left is c*cos(wn*t) = 0. Since cos(0)= 1 (when t = 0) you know that c must equal 0 in order to make the expression true.
If no forces other than mg=N act in the vertical direction and the disk rolls freely, then what is would make the disk possibly slip?
If the disk is displaced a large distance from the equilibrium state, the force in the x-direction will be large. This will cause the disk to move very quickly and thus causing slippage.
i am still having trouble finding C and S, any tips?
Post a Comment