Question

the angular frequency of a motion whose equation is 4d^2y/dt^2 +9y = 0 is (y=displacement and t=time)?

Answer 1

motion of a body is described by equation $4\frac{d^2y}{dt^2}+9y=0$

or, $\frac{d^2y}{dt^2}+\frac{9}{4}y=0$

or, $\frac{d^2y}{dt^2}+\left(\frac{3}{4}\right)^2y=0$ it seems like motion of body is in simple harmonic motion,
because this equation is similar of $\frac{d^2y}{dt^2}+\omega^2y=0$
where $\omega$ is angular speed.

now compare both equations.
we get, $\omega^2=\left(\frac{3}{4}\right)^2$

$\omega=\pm\frac{3}{2}$ rad/s

hence, angular speed or angular frequency of motion is ±3/2 rad/s