A block of mass m is supported by a massless plate; an infinite network of massless plates and springs of constant K is connected beneath it as shown. Find X + Y in the source angular-frequency expression. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A block of mass m is supported by a massless plate; an infinite network of massless plates and springs of constant K is connected beneath it as shown. Find X + Y in the source angular-frequency expression. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Define equivalent stiffness kₑff of an infinite network viewed from its top plate. Step 2 — Because the network repeats, the lower portion has the same equivalent stiffness kₑff; replace it by one effective spring. Step 3 — Combine adjacent spring constants using series law kₛ = k₁k₂/(k₁+k₂), and parallel law kₚ = k₁+k₂. Solve resulting self-consistency equation for kₑff > 0. Step 4 — Use ω = √(kₑff/m). The PDF prints X+Y = 7. QUALITY FLAG — Actual repeating network diagram and source…