A mass 0.9 kg, attached to a horizontal spring, executes SHM with an amplitude  . When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude  . If the ratio   is  , then the value of   will be____

Explanation

Given:

• Initial mass, m₁ = 0.9 kg
• Additional mass, m₂ = 0.124 kg
• Amplitude ratio formula: (A'/A) = sqrt(m1 / (m1 + m2))

Step 1: Calculate Total Mass

m total = m₁ + m₂ = 0.9 kg + 0.124 kg = 1.024 kg 

Step 2: Compute Amplitude Ratio 

(A'/A) = sqrt(0.9 / 1.024) ≈ 0.9375

Final Answer

The new amplitude A' is approximately 93.75% of the initial amplitude A.