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If the collision occurs at time t0 = /(2 ), then the value of 4b2/a2 will be .
4.25
At t0 = 2 : v1 = v2 = 0 and each particle is at its extreme, displaced a from its mean position (spring at maximum extension).
Velocities exchange: v2 = a 2, v1 = 0 vcm = a 4.
In the CM frame: v2' = + a 4, v1' = - a 4, displacement of each from its mean = a.
Amplitude: b2 = a2 + ( v' )2 = a2 + a216 = 17a216
4b2a2 = 174 = 4.25
Answer: 4.25
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