A block of mass m is attached to three springs A, B and C with force constants k, k and 2k as shown. It is slightly pushed against spring C. If angular frequency is √(Nk/m), find N. The surface is smooth.

Question

G1 Physics · Accepted Answer

For a small displacement along the allowed direction, resolve the extensions of the three springs. The two k springs and the 2k spring together give an effective restoring constant 3k along the displacement. Thus ω²=kₑ/m=3k/m. Since ω=√(Nk/m), N=3.