Question

Find the angular frequency of a mass attached to a spring, kept on a horizontal frictionless surface.

Answer 1

Let the mass be displaced by $x$ from the equilibrium position as shown.
Writing the force equation,
$F=-kx\Rightarrow m\frac{d^{2}x}{d{t}^2}=-kx\Rightarrow \frac{d^{2}x}{d{t}^2}=-\left(\frac{k}{m}\right)x$
Comparing with the standard equation, we get
${\omega }^2=\frac{k}{m}\Rightarrow \omega =\sqrt{\frac{k}{m}}$