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  4. A body executing linear simple harmonic motion has a velocity of 3 ms -1 when its displacement is 4 cm and a velocity of 4 ms -1 when its displacement is 3 cm. What is the amplitude of oscillation ?

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Q. A body executing linear simple harmonic motion has a velocity of $3\, ms ^{-1}$ when its displacement is $4\, cm$ and a velocity of $4\, ms ^{-1}$ when its displacement is $3 cm$. What is the amplitude of oscillation ?

Bihar CECEBihar CECE 2009Oscillations

Solution:

Velocity of SHM $v=\omega \sqrt{a^{2}-y^{2}}$
$\Rightarrow 9=\omega^{2}\left[a^{2}-16\right]$ ...(i)
Similarly, $16=\omega^{2}\left[a^{2}-9\right]$ ...(ii)
Dividing Eq. (ii) by Eq. (i), we get
$\frac{16}{9}=\frac{\left[a^{2}-9\right]}{\left[a^{2}-16\right]}$
$\Rightarrow a^{2}=25$
or $a=5\, cm$