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## New answers tagged spring

1

Here are the steps you can take. Degrees of Freedom. There are 3 degrees of freedom, one for the base plate, one for the box and one for the mass. Hence there are 3 variables that you need to track, as well as their derivatives. I will name them $x_0=\gamma(t)$ for the plate, $x_1$ for the box and $x_2$ for the ball. Free Body Diagrams. For the moving ...

0

The behavior of the system (not surprisingly)depends on the initial conditions. (For the sake of argument, we can assume the box starts stationary with respect to the table and $\gamma(0)=0$) I am assuming the problem is $1d$; this way we will end up with two coupled equations of motion. Let's show the box's coordinate with $\chi$ and ball's coordinate with ...

0

Force is just minus gradient of U. Gradient is just (spatial) derivative. $F=-\frac{d}{dx}\frac{kx^2}{2}=-\frac{2xk}{2}=-kx$ So, if your task has "differential" nature, it will probably suitable for force method. And if your task has "integral" nature, then it will probably suitable for potential method.

0

In problems like this, it's easier to work with a specific case as opposed to the general one. Let's assume that the original spring has 12 coils. Then each of the cut springs would have 3 coils. Let's say that applying a 12 N force to the original spring would compress it 12 cm. Now let's apply some force, Y, to the spring that was cut (has 3 coils). This ...

4

In a sense yes, if you're very careful about what you're holding constant. Stating that a variable is proportional to another variable implies that all other relevant quantities are being held constant. For example, there's a simple relation $d=vt$ that describes the distance $d$ something travels in a time $t$ when traveling at speed $v$. One might say ...

3

You have to be a little careful to make sure you're clear on what you're modeling when you combine various equations together. If you are thinking of a mass attached to a spring attached to the ceiling, then yes, the mass is proportional to the spring displacement. This follows since in the case of an object being acted on by gravity, $a=g$, and thus ...

0

You need to take your attempt a little further, rather than just resolving the various forces: Try setting up a differential equation for your problem, you know that the particle is oscillating so you can propose a trial solution to your equation (something along the lines of $y=Ae^{ix}$)

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