A body of mass 1 kg is suspended from a weightless spring having force constant 600 N m⁻¹. Another body of mass 0.5 kg moving vertically upwards hits the suspended body with a velocity of 3.0m s⁻¹ and gets embedded in it. Find the frequency of oscillations and amplitude of motion.
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Question

A body of mass 1 kg is suspended from a weightless spring having force constant 600 N m⁻¹. Another body of mass 0.5 kg moving vertically upwards hits the suspended body with a velocity of 3.0m s⁻¹ and gets embedded in it. Find the frequency of oscillations and amplitude of motion.

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G1 Physics · Accepted Answer

After impact the bodies stick, so total mass is 1.5 kg and ω=√(600/1.5)=20 rad s⁻¹; hence f=10/π Hz. Momentum conservation gives common upward speed v=(0.5×3)/1.5=1 m s⁻¹. Measuring from the new equilibrium and using A²=x₀²+(v/ω)² gives A=5√37/6 cm. Therefore all listed statements are correct.