A particle moves along a straight line to follow the equation a x2+b v2=k, where a, b and k are constants and x and v are x-coordinate and velocity of the particle respectively. Find the amplitude.

Question

A particle moves along a straight line to follow the equation a x2+b v2=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) √(k/b) (B) √(b/k) (C) √(a/k) (D) √(k/a)

Tardigrade Admin · Accepted Answer

a x2+b v2=k b v2=k-a x2 v2=(k/b)-(a/b) x2 Compare with v2=A2 ω2-ω2 x2 ω2=a / b and A2 ω2=k / b A=√(A2 ω2/ω2)=√(k / b/a / b)=√(k/a)

Q. 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.

$\frac{k}{b}$

$\frac{b}{k}$

$\frac{a}{k}$

$\frac{k}{a}$

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

Q. A particle moves along a straight line to follow the equation ax2+bv2=k, where a,b and k are constants and x and v are x-coordinate and velocity of the particle respectively. Find the amplitude.

bk​​

kb​​

ka​​

ak​​