The problem is attached.
I think you can solve it generally using the relationships:
Δtotal = ½(Δ1 + Δ2)
assuming the mass is located at mid-span.
The statement "If K1 = K2, Ktotal = K1 + K2" implies that there is no flexibility in the beam. The post title suggest that you want the stiffness to reflect the stiffness of the beam as well. Which is it?
The equivalent spring constant Ktot = k1 + k2 no matter the values of k1 or k2. They follow the same rules as resistors.
Parallel & Series springs:
I'll disagree on this. The parallel springs formula assumes that both springs displace the same. Here, however, the springs will displace differently to maintain equilibrium. Therefore, a unique formula needs to be derived.
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