Problem 5: A body of mass m suspended from a spring with spring constant k vibrates with f₁. When its length is cut into half and the same body is suspended from one of the halves, the frequency is f₂. Find out f₁/f₂.

Answer

Given data               Mass suspended = m           spring constant = k         

Full length frequency = f₁     Half length frequency = f₂

Required                         f₁/f₂

Formula

Theory                     Let the displacement of the whole length spring = x

                                When the spring is cut into two, the displacement is = x/2                                 Similarly,

Put this value of k in the formula and find time period for the full length.

And the frequency is

Similarly, for the half length of the spring, the time period is

And the frequency is

Now to find the ration f₁/f₂,

Thus the frequency of the oscillation decreases when the length of the pendulum is decreased.