# Simple Harmonic Motion: Equivalent force constant of springs

Two springs with the same unstretched length, but different force constants and are attached to a block with mass on a level, frictionless surface. Calculate the effective force constant in each of the three cases depicted in the figure.

a). Express your answer in terms of the variables k1, m, k2

k_eff -c =

b) An object with mass , suspended from a uniform spring with a force constant , vibrates with a frequency . When the spring is cut in half and the same object is suspended from one of the halves, the frequency is . What is the ratio ?

Express your answer in terms of the variables k and m

**Any solution I have attempted to part B has prompted an automatic response of "answer does not depend on the variable k or m" Which confuses me to no end.

Any help on this problem would be VERY appreciated.

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#### Solution Summary

Two springs connected in three different ways, the equivalent force constant is calculated.

The ratio of the new and initial frequencies is calculated when the spring of the oscillator is cut in two equal parts.