How to calculate the potential energy of a spring?

[haruspex]

Why horizontal though?

The forces in the horizontal direction cancel each other ( If we assume that both of the springs have a constant of k) and the net force in the y direction. So It will only move vertically...?

Horizontal plane. That is, the diagram may be as viewed from above.

 

[ramialsaiad]

No, you cannot express it purely in terms of x except by solving the differential equation.
What is the whole question? You originally said you wanted to find the potential energy, which you have done. Why is the KE of interest? Do you need to find the equation of motion?

Also, I see you have reintroduced mgx. That is applicable if the motion is in the vertical plane, but not if it is in the horizontal plane. Do you know which plane it is in? If the question does not state, I would assume it is horizontal, and throw away the mgx term.

I have to find KE , it is required ..
I do want to find the equation of motion in terms of x for KE and PE and the force on the brick as a function of x ..
Iam sure it is moving in vertical direction ..

 

[haruspex]

I have to find KE , it is required ..
I do want to find the equation of motion in terms of x for KE and PE and the force on the brick as a function of x ..
Iam sure it is moving in vertical direction ..

Ok, if you are sure it is vertical keep the mgx.
What type of motion do you think it will be?

 

[ramialsaiad]

Ok, if you are sure it is vertical keep the mgx.
What type of motion do you think it will be?

potential energy and I got it correct as you said before

 

[haruspex]

potential energy and I got it correct as you said before

Not sure what question you are answering. I asked what kind of motion you thought would result.

 

[ramialsaiad]

Not sure what question you are answering. I asked what kind of motion you thought would result.

no idea

 

[haruspex]

no idea

In the simpler case of a mass hanging from a spring, or lying on a smooth table and connected to a horizontal spring, what type of motion occurs?

 

[ramialsaiad]

In the simpler case of a mass hanging from a spring, or lying on a smooth table and connected to a horizontal spring, what type of motion occurs?

potential energy

 

[haruspex]

potential energy

That is not a type of motion. Here are some types: constant velocity, constant acceleration, elliptical orbit, simple harmonic motion. Pick one.

 

[ramialsaiad]

That is not a type of motion. Here are some types: constant velocity, constant acceleration, elliptical orbit, simple harmonic motion. Pick one.

simple harmonic motion

 

[haruspex]

simple harmonic motion

Right. Can you write the generic form of the equation for that? If so, try that out as a solution to your differential equation.

 

[ramialsaiad]

Right. Can you write the generic form of the equation for that? If so, try that out as a solution to your differential equation.

I do not know how to do ?
if you can provide the starting equation to me that will be nice ,, then I try to go further

 

[haruspex]

I do not know how to do ?
if you can provide the starting equation to me that will be nice ,, then I try to go further

I find it very strange that you have been given a problem in harmonic motion yet appear to know so little about it.
The general form of the solution is $x=A\sin(\omega t+\phi)$, where A is the amplitude, ω is the frequency and φ is the phase. Or you can use cos instead of sin, which changes the value of φ but keeps all else the same.