Finding the differential equation for a oscillating system

[JustinLiang]

Homework Statement

The Attempt at a Solution

I don't think this is the correct answer because for some reason I have a constant mg term. Usually I get mgsinθ and from small angle approximations it becomes mgθ, but this time I am getting mgcosθ and from small angle approximations it becomes mg.

What am I doing wrong? Or is this correct?

 

[haruspex]

I don't see the distances in your expressions for the moments.

 

[theBEAST]

I don't see the distances in your expressions for the moments.

I just tried this question and did it with the distances, but I also don't understand why there is a constant term. That term is throwing me off.

 

[haruspex]

I just tried this question and did it with the distances, but I also don't understand why there is a constant term. That term is throwing me off.

Please post your working if you'd like further assistance.

 

[Nickie]

Dear student,

Thank you for reaching out for assistance with your homework problem. It is important to understand that there is not one single differential equation for all oscillating systems. The specific form of the differential equation will depend on the specific system and its parameters, such as mass, spring constant, and damping coefficient. Therefore, it is difficult to determine if your equation is correct without knowing the specific system you are working with.

However, in general, the differential equation for a simple harmonic oscillator is given by m(d^2x/dt^2) + kx = 0, where m is the mass of the object, k is the spring constant, and x is the displacement from equilibrium. This equation can be derived using Newton's second law and Hooke's law. It is possible that in your derivation, you may have made a small mistake or used different assumptions, resulting in a slightly different form of the equation.

I would recommend carefully reviewing your derivation and checking your assumptions to ensure the accuracy of your equation. You can also compare it to the general form mentioned above to see if they are consistent. If you are still unsure, it may be helpful to consult with your instructor or a classmate for further clarification.

I hope this helps and wish you success in solving your homework problem.

Sincerely,