Question

Three similar oscillators, A, B, C have the same small damping constant $r$, but different natural frequencies ${\omega }_0=(k/m{)}^{\frac{1}{2}}:1200Hz,1800Hz,2400Hz$. If all three are driven by the same source at $1800Hz$, which statement is correct for the phases of the velocities of the three?

• A. ${\varphi }_A={\varphi }_B={\varphi }_c$
• B. ${\varphi }_A<{\varphi }_B=0<{\varphi }_c$
• C. ${\varphi }_A>{\varphi }_B=0>{\varphi }_c$
• D. ${\varphi }_A>{\varphi }_B>0>{\varphi }_c$

Answer 1

The correct option is A ${\varphi }_A={\varphi }_B={\varphi }_c$

$tan\varphi =\frac{\omega L-\frac{1}{\omega C}}{R}$
If $\omega <{\omega }_0⟹$ circuit is capacitive
$⟹$ it leads voltage
$⟹$ velocity leads force.
if $\omega ={\omega }_0\varphi =0$
if $\omega >{\omega }_0$ velocity lags behind force.