Oscillations - mass suspended from string

[desmond iking]

Homework Statement

the answer is a for this question. but i don't understand how to get the solution.

Homework Equations

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)

 

[NascentOxygen]

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.

 

[desmond iking]

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.

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

 

[Orodruin]

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

 

[desmond iking]

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

can you explain further?

 

[NascentOxygen]

can you explain further?

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’’ )

 

[NascentOxygen]

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

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??

 

[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.