9000024807

SubArea:

Level:

Project ID:

9000024807

Accepted:

Clonable:

Easy:

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 π \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} + 3 l_{1}

The length doubles, i.e.

l_{2} = 2 l_{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} - 3 l_{1}

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