Oscillations - mass suspended from string

1. Jun 21, 2014

desmond iking

1. The problem statement, all variables and given/known data
the answer is a for this question. but i dont understand how to get the solution.

2. Relevant equations

3. The attempt at a solution
mg-k(l-a+b)=ma

since mg=k(l-a)

-kb=ma

a=-(k/m)b

k/m=a/b

so my ans is sqrt root( a/b)

Attached Files:

• IMG_20140621_074427[1].jpg
File size:
47.1 KB
Views:
83
2. Jun 21, 2014

Staff: Mentor

Hi, desmond. Welcome to the forum.

a, b, and l are constants, so the equation you came up with shows a fixed, constant acceleration. As you realize, this isn't correct; a fixed acceleration is not a characteristic of oscillatory motion. Somewhere in that equation you'd need a variable x which is the extension at any moment.

It might be easier if you were to start with the options, and maybe eliminate them one by one? Look for a reason why any particular option could not be the formula for ω2.

Last edited: Jun 21, 2014
3. Jun 22, 2014

desmond iking

so if the option of (a/b) is given, can i choose it?

4. Jun 22, 2014

Orodruin

Staff Emeritus
Try getting to the differential equation given in the problem by considering what forces are acting on the mass for an arbitrary displacement.

5. Jun 22, 2014

desmond iking

can you explain further?

6. Jun 22, 2014

Staff: Mentor

Do you understand the mathematics behind x with a pair of dots above it, as it appears in the textbook question in your attachment? (Sometimes it is written x’’ )

Last edited: Jun 22, 2014
7. Jun 22, 2014

Staff: Mentor

Choose it if you wish. It's wrong though.

Oh, I just noticed: aren't you using the letter "a" for two different things in your equations in this thread??

Last edited: Jun 22, 2014
8. Jun 22, 2014

rude man

Hint: determine the spring constant k, then use the formula for radian frequency w of a mass bobbing up & down:
w = w(k,m).

If you don't know the formula you'll have to proceed per post #4.