Two springs are attached end-to-end to a green box of mass M as shown in the fig
ID: 2270444 • Letter: T
Question
Two springs are attached end-to-end to a green box of mass M as shown in the figure. Determine an expression that gives the period T of motion for the box attached to this combination of springs. The two individual springs have spring constants of k1 and k2, respectively.
Two springs are attached end-to-end to a green box of mass M as shown in the figure. Determine an expression that gives the period T of motion for the box attached to this combination of springs. The two individual springs have spring constants of k1 and k2, respectively.Explanation / Answer
Assume forces F1 and F2 acting on spring k1 and k2 respectively.
Assume the displacement produced in the spring 1 is x1 and spring 2 alone is x2;
The total displacement = x1+ x1 of the block
Hence the net focrce on block is k(x1+x2); where k is the net spring constant
force on block = F2
Force on spring = F2 = k2*x2
Force on spring 1 = F1 = k1*x1
but both are massless springs F1 = F2 ; implies x1= k2 x2/k1
using x1+ x2 = x; we get x = x2*(k1+k2)/k1
Hence force on block = [k2*(k1)/(k1+k2)]*x
implies net spring constant = (k1*k2)/(k1+k2)
Time preiod T = 2pi sqrt(M/k) = 2*pi *sqrt(M*(k1+k2)/(k1*k2))
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