Question

Write out the (relevant) equations of motion for the following system (shown in the figure below) when:

(a) A and B are both free. (b) A is clamped. (c) B is clamped. (Assume A moves along the line of the springs.)

Answer 1

Since the figure is missing then the equation of motion (in general case)

$\Sigma F=ma\to \Sigma F=m\frac{d^2x}{dt^2}$

$\Sigma F$ is the sum of all forces acting on the body;

$m$ is the mass of the body;

$x$ is the body coordinate.