Question

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

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

Answer 1

Answer: (A)

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 $a=5cm$