Question

Which one of the following represents simple harmonic motion?

• A. $x^2=a+bv$
• B. $x=\sqrt{a^2+b{v}^2}$
• C. $x=a-bv$
• D. $x=\sqrt{a^2-b{v}^2}$

Answer 1

The correct option is D $x=\sqrt{a^2-b{v}^2}$

Relation (d) which is $x=\sqrt{a-b{v}^2}$ correctly represent the SHM because, velocity

$v=\omega \sqrt{a^2-x^2}$

or $x=\sqrt{a^2-v^2/{\omega }^2}$

or $x=\sqrt{a^2-b{v}^2}$

where $b=\frac{1}{{\omega }^2}$