If the stiffness coefficients of two spring oscillators are K1 and K2, and a mass of M is hung after they are connected, what is the period of the system
After applying force F to two connected oscillators, the force on both oscillators is f, and the total deformation x = X1 + x2 = f / K1 + F / K2 = f (1 / K1 + 1 / K2)
Let the stiffness coefficient of the system be K
F=kx=k[F(1/k1 +1/k2)]
k=1/k1 +1/k2=k1*k2/(k1+k2)
Let the angular frequency of the system be w
w^2=k/M=k1*k2/[M(k1+k2)]
The period is
T = 2 / w = 2 * radical [M (K1 + K2) / (K1 + K2)]
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