How to Solve Pendulum Forces in Component Form?

[JaySean]

Homework Statement

Hi, I need help in solving question c) (a pendulum) The required data, problem and relevant equation is in the picture

The Attempt at a Solution

I am not sure how to solve it but here are my thoughts:
since mg is working at j
y(t)j= mg
does that mean K(r-L0) x(t) direction?
I am not sure how to start/think to solve this problem so any tips will be helpfull, thanks!

 

[Brian T]

Look at the vector attached to the second term. It is not in the i / x direction but rather in the r direction. It acts directed from the radius of the pendulum. What law describes this force?

Also, think why do we divide the r vector by its magnitude?

 

[JaySean]

Look at the vector attached to the second term. It is not in the i / x direction but rather in the r direction. It acts directed from the radius of the pendulum. What law describes this force?

Also, think why do we divide the r vector by its magnitude?

Is it Hookes law?
I assume we divide r vector by its magnitude to determine the direction of the force

 

[lightgrav]

the rope stretches along its length like a spring. all c) asks you to do is split the diagonal Force into (x,y) components.

 

[JaySean]

Is mg=y component correct or is it wrong?
And what force is working in the x direction? Or did I misunderstand what the task is asking for?

 

[lightgrav]

mg is entirely vertical ... but most folks treat "up" as positive.
That is not the ONLY vertical Force contribution, however. The diagonal (spring) Force has x-component and y-component.

 

[JaySean]

So K(r-L0) works both in x and y direction? Am I then supposed to split the force and find which force works in x and y direction?

 

[lightgrav]

the wording in part c) could not be more explicit.

 

[JaySean]

r(t)=(K*r)i-K*L0j would this be correct?

 

[JaySean]

bump