7.4.35 | before revision #12872 | Savchenko Solutions

Statement

7.4.35^∗. What is the period of small vibrations of four charged bodies connected by
identical filaments of length l and moving as shown in the figure? Mass and
charge of the body m and q.

Example Statement:
$$1.1.1.$$ Determine the coordinate $$x(t)$$ of a body as a function of time $$t$$ , given that its acceleration is defined as $$a(t) = bt$$ , where $$b$$ is a constant.

Solution

[Your solution should be placed here]

Example Solution:
The acceleration of the body defined by

$$$a(t) = bt$$$

We know that acceleration is the time derivative of velocity:

$a(t) = \frac{d v(t)}{d t}$

To find the velocity $$v(t)$$ , we integrate $$a(t)$$ with respect to time:

$v(t) = \int a(t) \, dt = \int b t \, dt$

If the initial velocity is $$v(0) = 0$$ , then the velocity becomes:

$v(t) = \frac{b t^2}{2}$

Likewise, integrate $$v(t)$$ with respect to time:

$x(t)= \int v(t) \, dt = \frac{b}{2} \int t^2 \, dt$

From where the coordinate from time, considering the initial conditions:

$\boxed{x(t)=\frac{bt^3}{6}}$

Answer

[Insert a concise answer or boxed result, like this:]

Example Answer:
$x(t)=\frac{bt^3}{6}$