Question

Conceptual question about the oscillation of a point on a string as a sinusoidal wave propagates along it...(pic inside)

Answer 1

For (a) I got the time point A moving upward with max speed is at 2/8T, and I'm fairly certain that's right, but the answers given in the book for (b) and (c) are confusing me a little bit.

For (b), it asks which time point B has the greatest upward acceleration. I thought it has the greatest upward acceleration when it's at equilibrium on it's way to a positive y-value, being at time=2/8T, but the book says it's 4/8T. Anyone know why?

Same for (c), I thought if it has a downward acceleration but an upward velocity, the derivative of the position would be positive and the derivative of the velocity would be negative, but the book says the answer is at time=5/8T.

Can anyone kinda walk me through (b) and (c)?

Answer 2

for b you gave the answer. at 2t/8, the point B is moving towards -ve y axis.

Answer 3

At t=0, isn't it at -y though? So I thought at t=2/8T, it would be at y=0, moving towards y=+y?

Answer 4

cartesian plane looks like this no?

Answer 5

Oh, wow, I'm in idiot. I was thinking of point (c), not point (b). But wouldn't the greatest acceleration for (b) be at 6/8T, when it's at y=0, going from -y to +y?

Answer 6

My professor told me the book gave the wrong answer for either question (b) or (c), and he said he'd give bonus points to who can tell him which one and why.

Answer 7

look, for the maximum acceleration, velocity, i always take help of the formulas when i get confused. so acceleration for shm is w^2*y right? where is this maximum? where is y maximum? at extreme position.
for a conceptual approach, you have to give me 15 mins or so.

Answer 8

and i dont think any of the answers is wrong. the answer to c is 5t/8.

Answer 9

for point B, at t=o upward velocity is 0. now it has to move down. its acc increases and increases till the time 4t/8, where it cannot go down anymore, its downwards velocity is 0, and the acc. is maximum.

Answer 10

Yea, both of those answers make sense to me. I don't know why my professor said one of them was wrong. I'll let you know.

Thanks for the help, I appreciate it.

Answer 11

You're welcome.