Homework Help: Damped and Forced Harmonic Motion

1. Feb 11, 2012

FeDeX_LaTeX

1. The problem statement, all variables and given/known data
http://desmond.imageshack.us/Himg812/scaled.php?server=812&filename=quesq.jpg&res=medium [Broken]

2. Relevant equations
F = ma, F = -kx, SHM equations

3. The attempt at a solution

Here's the diagram they've done for part (b).

http://desmond.imageshack.us/Himg844/scaled.php?server=844&filename=ansr.jpg&res=medium [Broken]

I'm not understanding why the 6mkv force is shown acting upwards; surely if the string is going to move up, and the water is a resistive force, then it would act downwards?

And why is the acceleration downwards? I thought it would accelerate towards the point where it reaches (x+e) where the particle would be at maximum velocity, or am I thinking of springs?

Thanks.

Last edited by a moderator: May 5, 2017
2. Feb 12, 2012

vela

Staff Emeritus
Considering there's an obvious mistake in the equation given in part (b), I wouldn't put too much faith in there not being other obvious errors. You're right. For the situation described, the acceleration should be upward and the damping force, downward. Also, note that the figure shows x being the distance from the lower dotted line to some arbitrary depth below, but it should be from the dotted line to the location of P. The figure is a mess.

3. Feb 13, 2012

FeDeX_LaTeX

Okay, thanks. I thought I was going to have a mental breakdown.

4. May 14, 2012

FeDeX_LaTeX

I'm bumping this because the exam is getting closer and I'm still not sure about this. I don't think this is a mistake, and I'm perhaps just missing something crucial. Every question in the textbook has the resistive force acting in the direction of motion and acceleration (seemingly) pointing the opposite direction. Now I am confused.

-It's SHM, right? So acceleration acts towards the centre of motion which is UPWARDS.
-Resistive force should therefore be acting downwards.

Are the above two statements correct?

EDIT: I re-did the question, with acceleration upwards and resistive force downwards. Got a negative co-efficient for the 6k dx/dt (the m in their 'show that' question is an error, it should cancel). So the resistive force is causing the problem. Ugh. I can't get their equation no matter what I do.

Last edited: May 14, 2012
5. May 14, 2012

vela

Staff Emeritus
You originally asked about the drawing, which is indeed a mess. The equation, however, is fine, other than the extra m. What does Newton's second law tell you $m\ddot{x}$ is equal to?