Question

From the differential equation, $\frac{d^{2}x}{d{t}^2}+16x=0$
(1) we can find time period of oscillation
(2) we cannot find time period of oscillation
(3) we cannot find initial phase of oscillation
(4) we cannot find frequency of oscillation.

• A. 1 & 2
• B. 2 & 3
• C. 1 & 3
• D. 1, 2 and 3

Answer 1

The correct option is C 1 & 3

$\frac{d^{2}x}{d{t}^2}+16x=0or\frac{d^{2}x}{d{t}^2}=-(4{)}^{2}x$
Here $\omega =4$
$\therefore T=\frac{2\pi }{\omega }=\frac{\pi }{2}s$
Initial phase depends on the position of particle at and direction of velocity of the particle, which we can’t obtain from the above equation.