[Figure: (A) a block of mass m on a frictionless floor with a block of mass 2m fixed on top of it, joined by a spring of constant k to a wall on each side; (B) a block of mass m on a frictionless floor, joined by a spring of constant k to the left wall and a spring of constant 2k to the right wall.…

Question

[Figure: (A) a block of mass m on a frictionless floor with a block of mass 2m fixed on top of it, joined by a spring of constant k to a wall on each side; (B) a block of mass m on a frictionless floor, joined by a spring of constant k to the left wall and a spring of constant 2k to the right wall.] In figure (A) a mass 2m is fixed on a mass m which is attached to two springs each of constant k. In figure (B) a mass m is attached to two springs of constants k and 2k. The masses in (A) and (B) are each displaced horizontally through x and released. The time periods T₁ and T₂ of (A) and (B) satisfy

Accepted Answer

(1) (T₁)/(T₂)=3/(√2). In (A) the two springs act in parallel, k_A=2k, and the oscillating mass is m+2m=3m: T₁=2π√(3m)/(2k). In (B) the springs are again in parallel, k_B=k+2k=3k, with mass m: T₂=2π√m/(3k). (T₁)/(T₂)=√(3m)/(2k)×(3k)/m=√9/2=3/(√2).

Step-by-step solution

Why the other options are wrong