A block of mass 0.9 kg attached to a spring of constant k lies on a frictionless floor. The spring is compressed by √2 cm and the block is at a distance 1/√2 cm from a wall. On release it collides elastically with the wall and the period of motion is 0.2 s. Find k approximately.

Question

G1 Physics · Accepted Answer

The initial compression is A=√2 cm. The wall is at a distance 1/√2 cm from the initial block position, so collision occurs at x=-A/2. From an extreme to x=-A/2 takes phase π/3. Elastic reflection makes the return symmetric, so the complete repeated motion has period 2(π/3)/ω=0.2 s. Thus ω=10π/3 rad s⁻¹ and k=mω²≈0.9(10π/3)²≈98.7 N m⁻¹≈100 N m⁻¹.