A block of mass m placed on a smooth horizontal surface is attached to a spring and is held at rest by a force P in equilibrium as shown (at equilibrium compression in spring is l₁). Suddenly the force P changes its direction opposite to the previous one. If the maximum extension of the spring during the subsequent motion is l₂ then find l₂/l₁ = ?
Physics · Mixed Chapter
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Question

A block of mass m placed on a smooth horizontal surface is attached to a spring and is held at rest by a force P in equilibrium as shown (at equilibrium compression in spring is l₁). Suddenly the force P changes its direction opposite to the previous one. If the maximum extension of the spring during the subsequent motion is l₂ then find l₂/l₁ = ?

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Initially, compression l₁ is maintained by P=kl₁, so the initial spring coordinate is −l₁. Step 2: After P reverses, the new equilibrium is at extension +l₁. The mass is released from rest at −l₁, a displacement 2l₁ from the new equilibrium. Step 3: Its oscillation amplitude about +l₁ is 2l₁. Hence the greatest extension from natural length is l₂=l₁+2l₁=3l₁. Step 4: l₂/l₁=3.