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Look at the values near t = 0.

At t = 0, cos(0) is +1, and since the graph shows y₂(0) is positive, then a₂ must be positive.

For small values of b₁t, sin(b₁t) ≈ b₁t.  For b₁ positive, this is positive, and since the graph shows y₁(t) positive for small values of t, then a₁ must be positive.

a₁ and a₂ represent the amplitudes of y₁ and y₂ respectively.  Since it is clear from the graph that the amplitude of y₁ is greater than that of y₂, we must have a₁>a₂.

Summarising:    0 < a₂ < a₁

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