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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
A body executing $S.H.M.$ along a straightline has a velocity of $3 \,ms ^{-1}$ when it is at a distance of $4 \,m$ from its mean position and $4 \,ms ^{-1}$ when it is at a distance of $3 \,m$ from its mean position. Its angular frequency and amplitude are
  • A
    $2 \,rad s ^{-1}$ and $5 \,m$
  • B
    $1 \,rad s ^{-1}$ and $10 \,m$
  • C
    $2 \,rad s ^{-1}$ and $10 \,m$
  • ✓
    $1 \,rad s ^{-1}$ and $5 \,m$
✓

Answer

Correct option: D.
$1 \,rad s ^{-1}$ and $5 \,m$
d
(d)

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

$v_1=3 \,m / s x_1=4 \,m$

$v_2=4 \,m / s x_2=3 \,m$

$3=\omega \sqrt{A^2-4^2} \ldots(i)$

$4=\omega \sqrt{A^2-3^2} \ldots(ii)$

Solving $(i)$ and $(ii)$, we get

$A=5 \,m$ and $\omega=1 \,rad / s$

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