9000024807
Level:
C
A body hangs on a string of the length
\(l_{1}\). The length
\(l\) of the spring
defines the period \(T\)
of motion by the relation
\[
T = 2\pi \sqrt{ \frac{l}
{g}},
\]
where \(g\)
is a standard acceleration of gravity. We have to adjust the length of the string such
that the period doubles. Find the new length of the string.
We elongate the string by \(3\cdot l_{1}\),
i.e. \(l_{2} = l_{1} + 3l_{1}\).
The length doubles, i.e. \(l_{2} = 2l_{1}\).
The new length will be half of the original length, i.e.
\(l_{2} = \frac{1}
{2}l_1\).
We shorten the string by \(3\cdot l_{1}\),
i.e. \(l_{2} = l_{1} - 3l_{1}\).