Answer confirmation-not an assignment question.

[rsaad]

Hi! I have attached the picture. Can someone please tell me what equation of motion will be?
My guess is that it will be

$\ddot{x}$ = -k/x -kx/2

 

[mfb]

What is x? What is "O"? What is fixed, what is not?
Those things labelled "k" are springs?
I don't think your answer is correct.

 

[Chestermiller]

Note that the springs are pulling in opposite directions. Check your signs.

 

[mfb]

I think the signs are right, but it depends on the (unknown) original problem. However, an x in the denominator looks odd and I would expect to see a mass in the equation.

 

[PJC01]

m

Hi there! Your guess is actually quite close. The equation of motion for this system would be:

m\ddot{x} = -kx - \mu\dot{x}

Where m is the mass, k is the spring constant, x is the displacement, and \mu is the coefficient of friction. This equation takes into account the effects of both the spring force and the friction force on the motion of the object. It is a second-order differential equation, meaning it requires two initial conditions (such as initial position and velocity) to solve for a specific solution. I hope this helps!