The force on the block due to the spring is given by Hooke's law:
$x(t) = \int v(t) dt = \int (2t^2 - 3t + 1) dt$ The force on the block due to the
The acceleration of the block is given by Newton's second law: The force on the block due to the
$x(t) = \frac{2}{3}t^3 - \frac{3}{2}t^2 + t + C$ The force on the block due to the
$a = \frac{F}{m} = -\frac{k}{m}x$
A block of mass $m$ is placed on a frictionless surface and is attached to a spring with a spring constant $k$. The block is displaced by a distance $A$ from its equilibrium position and released from rest. Find the acceleration of the block at $t = 0$.
$x(2) = \frac{2}{3}(2)^3 - \frac{3}{2}(2)^2 + 2 = \frac{16}{3} - 6 + 2 = \frac{16}{3} - 4 = \frac{4}{3}$.