Oscillator on an inclined plane

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Homework Help Overview

The problem involves a mass-spring system on an inclined plane, where the spring is fixed at the top and the mass is displaced from its equilibrium position. The discussion focuses on finding the displacement as a function of time under two scenarios: one with friction and one without.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the equation of motion, questioning the inclusion of gravitational forces and friction in their formulations. There is an exploration of the correct equations to use and the complexity of solving them.

Discussion Status

Some participants have offered insights into the equations involved, while others express uncertainty about the gravitational force's role and the overall approach to solving the problem. There is no explicit consensus on the best method to proceed, but various perspectives are being explored.

Contextual Notes

One participant notes the absence of resources like the back of the book for reference, indicating a reliance on forum discussion for guidance. There is also mention of the complexity of the equations involved, suggesting a challenging problem setup.

Gallium
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A spring with force constant K and negligible mass has one end fixed at the top of an inclined plane making an angle theta with the horizonatal. A mass M is attached to the free end of the spring and pulled down a distance x_0 below the equilibirum position and released. Find the displacement from the equilibrium, position as a function of the time if the incline:
a) is frictionless
b) has a coefficient of friction mu
 
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so how I am stuck is that ma + cv + kx = 0 but that the frictional and/or gravitational component will alternatively retard or assist the motion.

Not looking for a handout, but I would like to know the proper eqns to use
 
huh? In your equation of motion, you are missing the gravitationnal force (or rather its component in the direction of the plane). The only difference between a) and b) will be that in a) you don't have the frictionnal "cv" term but in b) you do.

These equations are not easy to solve.. I hope you have their solution in your book or notes.
 
I don't have BOB (back of book) to consult, if I did then I wouldn't be here posting on an internet physics forum...

any smart people out there?
 
The equation ma + cv + kx = 0 is correct. The gravitational force is not needed in the equation since the equilibrium position is the postion the spring is in under normal conditions, i.e. already taking into account the gravitational force.

The only way I can think of to solve the equation is to solve it as a differential equation. Start by letting x = exp(r*t), and differential to find v and a, and substitute into the equation, then solve for r.

If your unfamiliar with differential equations and/or complex numbers, this is probably not the method your expected to use.
 

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