Question

Two massless springs with spring constant 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitude will be

• A. 1 : 2
• B. 3 : 2
• C. 3 : 1
• D. 2 : 3

Answer 1

Answer: (B)

3 : 2

Answer 2

$ω_1A_1 = ω_2A_2$

⇒ $\frac{A_1}{A_2} = \frac{ω_1}{ω_2}$

= $\sqrt{ \frac{k^2}{m^2}} \times \sqrt{ \frac{m_1}{k_1}}$

= $\sqrt{ \frac{9k}{100} \times \frac{50}{2k}}$

= $\frac{3}{2}$