A certain mechanism includes a set of two springs suspended parallel to each oth

Question

A certain mechanism includes a set of two springs suspended parallel to each other that act as a simple harmonic oscillator. Each spring has a spring constant of k (measured in N/m). A mass m could be attached either to one spring only or to both of them together. When two springs are combined the spring constant doubles. What is the ratioTi/ T2, where Ti is the period when the mass is attached to a single spring and Tz is the period when the mass is attached to a doubled spring? What is the ratio of frequencies, fi/ f? 5.

Explanation / Answer

Time period T1= 2*pi(m/k1)^1/2 and T2= 2*pi(m/k2)^1/2

where k2= 2k1

So, T1/T2= 2*pi(m/k1)^1/2 / 2*pi(m/k2)^1/2

So, T1/T2= 2*pi(m/k1)^1/2 / 2*pi(m/2k1)^1/2 = 1 / 1/(2)^1/2

So, T1/T2 = (2)^1/2

As f= 1/T,

So, f1/f2= T2/T1 = 1/(T1/T2) = 1 / (2)^1/2

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