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A mass 0.9 kg, attached to a horizontal spring, executes SHM with an amplitude $A 1$ . 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 $A 2$ . If the ratio $A 1 A 2$ is $α α − 1$ , then the value of $α 4$ will be____

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answer is 4.

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Detailed Solution

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.

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