Question

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 ?

• A. 5 cm
• B. 7.5 cm
• C. 10 cm
• D. 12.5 cm

Answer 1

Answer: (A)

5 cm

Answer 2

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 E (ii) by E (i), we get
$\frac{16}{9}=\frac{\left[a^{2}-9\right]}{\left[a^{2}-16\right]}$
$\Rightarrow a^{2}=25$
or $a=5\, cm$