Two springs, each with unstretched length 0.200 m , but with different force con

Question

Two springs, each with unstretched length 0.200 m, but with different force constants k1 and k2, are attached to opposite ends of a block with mass m on a level, frictionless surface. The outer ends of the springs are now attached to two pins P1 and P2, 0.100 m from the original positions of the ends of the springs (the figure (Figure 1) ). Let k1 = 1.80N/m , k2 = 5.80N/m , and m = 0.100

kg

Two springs, each with unstretched length 0.200 m, but with different force constants k1 and k2, are attached to opposite ends of a block with mass m on a level, frictionless surface. The outer ends of the springs are now attached to two pins P1 and P2, 0.100 m from the original positions of the ends of the springs (the figure (Figure 1) ). Let k1 = 1.80N/m , k2 = 5.80N/m , and m = 0.100 Find the length of each spring when the block is in its new equilibrium position after the springs have been attached to the pins. Find the period of vibration of the block if it is slightly displaced from its new equilibrium position and released.

Explanation / Answer

a)

Let the new equilibrium position be a distance x to the right of the original position.

F1 =F2

1.8*(0.1+x) =5.8*(0.1-x)

0.18+1.8x =0.58-5.8x

7.6x=0.4

x=0.05263 m or 5.263 cm

so lengths of each spring

L1 =0.1+0.05263

L1=0.15263 m or 15.26 cm

L2=0.1-0.05263

L2=0.04737 m or 4.737 cm

b)

T=2pi*sqrt[m/(K1+K2)

T=2pi*sqrt[0.1/1.8+5.8]

T=0.72 s

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