Question

If the amplitude of velocity of a particle acted by a force F = F₀ cos wt along x-axis is given by v₀ = $\frac{1}{(a\omega^{2}–b\omega + c)^{1/2}}$ where b²> 4ac. The frequency of resonance is –

• A. w = b/a
• B. b/2ª
• C. a/b
• D. a/2b

Answer 1

Answer: (B)

b/2ª

Answer 2

For resonance, v₀ ® ¥ (max)

\ (aw² – bw + c)^1/2 ® minimum

$\frac { \mathrm { d } } { \mathrm { d } \omega }$ (aw² – bw + c) = 0 ̃ 2aw – b = 0

̃ w = $\frac { \mathrm { b } } { 2 \mathrm { a } }$