Question

The angular frequency of motion whose equation is $9\frac{d^{2}y}{d{t}^2}+16y=0$ is

$(y$ is displacement and $t$ is time$)$

• A. $\frac{9}{4}\text{units}$
• B. $\frac{4}{9}\text{units}$
• C. $\frac{4}{3}\text{units}$
• D. $\frac{2}{3}\text{units}$

Answer 1

The correct option is C $\frac{4}{3}\text{units}$

Given $\frac{9d^{2}y}{d{t}^2}+16y=0$

$\Rightarrow \frac{d^{2}y}{d{t}^2}=-\frac{16}{9}y$

Comparing with equation for S.H.M.

$\frac{d^{2}y}{d{t}^2}=-{\omega }^{2}y$

$\Rightarrow {\omega }^2=\frac{16}{9}$

$\Rightarrow \omega =\frac{4}{3}\text{units}$