question_answer

If a simple harmonic motion is represented by \[\frac{{{d}^{2}}x}{d{{t}^{2}}}+\alpha x=0,\] its time period is                              [AIEEE 2005]

A)  \[\frac{2\pi }{\alpha }\]             

B)      \[\frac{2\pi }{\sqrt{\alpha }}\]  

C)  \[2\pi \alpha \] 

D)       \[2\pi \sqrt{\alpha }\]

Correct Answer: B

Solution :

[b] Given, simple harmonic is

..(i)

We know acceleration,      (ii)

From Eqs. (i) and (ii), we have

Or