Oscillator on an inclined plane

[Gallium]

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

 

[Gallium]

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

 

[quasar987]

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.

 

[Gallium]

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?

 

[asrodan]

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.