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