Identical point masses P and Q oscillate vertically on springs of constants k₁ and k₂. If both oscillators have equal maximum speeds, find the amplitude ratio Aᵩ/Aₚ.
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Question

Identical point masses P and Q oscillate vertically on springs of constants k₁ and k₂. If both oscillators have equal maximum speeds, find the amplitude ratio Aᵩ/Aₚ.

G1 Physics · Accepted Answer

Step 1: The maximum speed in SHM is vₘₐₓ = Aω. Step 2: For a mass-spring oscillator ω = √(k/m). Step 3: Equal maximum speeds imply Aₚ√(k₁/m) = Aᵩ√(k₂/m), because the masses are equal. Step 4: Cancel √m: Aₚ√k₁ = Aᵩ√k₂. Step 5: Rearrange: Aᵩ/Aₚ = √(k₁/k₂). Final answer: √(k₁/k₂), Option D.