Question

A particle moves along a straight line to follow the equation $a x^{2}+b v^{2}=k$, where $a, b$ and $k$ are constants and $x$ and $v$ are $x$-coordinate and velocity of the particle respectively. Find the amplitude.

• A. $\sqrt{\frac{k}{b}}$
• B. $\sqrt{\frac{b}{k}}$
• C. $\sqrt{\frac{a}{k}}$
• D. $\sqrt{\frac{k}{a}}$

Answer 1

Answer: (D)

$a x^{2}+b v^{2}=k$
$b v^{2}=k-a x^{2}$
$v^{2}=\frac{k}{b}-\frac{a}{b} x^{2}$
Compare with $v^{2}=A^{2} \omega^{2}-\omega^{2} x^{2}$
$\omega^{2}=a / b$ and $A^{2} \omega^{2}=k / b$
$A=\sqrt{\frac{A^{2} \omega^{2}}{\omega^{2}}}=\sqrt{\frac{k / b}{a / b}}=\sqrt{\frac{k}{a}}$