What Causes Oscillatory Motion in a Particle with a Constant Force?

[Rulonegger]

Homework Statement

A particle with mass m which can move only in one dimension, is subject to a constant force
$$F= \begin{cases}-F_{0} && x>0\\F_{0} && x<0\end{cases}$$ with $F_{0}>0$.
First I've got to say if there is a potential energy. Then i must solve the particle dynamics (i.e. find v(t) and x(t) for all t), finding the period of the oscillatory motion in terms of the mass m, the force $F_{0}$ and some amplitude coefficient A.

Homework Equations

Supposing that there is a potential U, it must satisfy that
$$\vec{F}=-\nabla{U}$$
just pointing out that the potential (if it exists) shouldn't be derivable in x=0, just like the function $|x|$.

The Attempt at a Solution

When i try to write down the equations of motion, and i solve for x, i get that the position is linearly proportional to the time t plus some quadratic dependence of the time, so i don't know where the oscillatory motion comes from.

 

[Dick]

Homework Statement

A particle with mass m which can move only in one dimension, is subject to a constant force
$$F= \begin{cases}-F_{0} && x>0\\F_{0} && x<0\end{cases}$$ with $F_{0}>0$.
First I've got to say if there is a potential energy. Then i must solve the particle dynamics (i.e. find v(t) and x(t) for all t), finding the period of the oscillatory motion in terms of the mass m, the force $F_{0}$ and some amplitude coefficient A.

Homework Equations

Supposing that there is a potential U, it must satisfy that
$$\vec{F}=-\nabla{U}$$
just pointing out that the potential (if it exists) shouldn't be derivable in x=0, just like the function $|x|$.

The Attempt at a Solution

When i try to write down the equations of motion, and i solve for x, i get that the position is linearly proportional to the time t plus some quadratic dependence of the time, so i don't know where the oscillatory motion comes from.

It's a force just like gravity, except when you cross x=0 gravity reverses. Write down a solution for x>0 and then match it onto one for x<0.

 

[Rulonegger]

Oscillation

Yeah, i see your comparison, but intuitively i think the motion should be like a sinusoidal function of time, but the period of oscillation is?

 

[Dick]

Yeah, i see your comparison, but intuitively i think the motion should be like a sinusoidal function of time, but the period of oscillation is?

If you throw a ball up in the air the time it takes to come back depends on how fast you throw it. Same thing with the period of oscillation here. It will depend on the initial position and velocity. Or you could calculate it as a function of the total energy.