Physics

Problem

A student builds a pendulum by suspending a small metal sphere from a light string of length

0.80\,\text{m}

in a physics laboratory where

g=9.8\,\text{m}\,\text{s}^{-2}

. The measured period of small-angle oscillation is

1.8\,\text{s}

. The student then lengthens the string to

1.20\,\text{m}

and repeats the experiment at the same location. (a) Determine the new period of oscillation at the same location. (b) Calculate the percent change in period produced by increasing the length of the pendulum.

Intuitive explanation

A simple pendulum's period depends only on its length and gravity through the relationship $T = 2\pi\sqrt{L/g}$ —not on the mass or amplitude. When you increase the string length, the period increases because the bob travels a longer path, even though gravity pulls it down with the same acceleration. Use the period formula to predict the new period, or compare the ratio of the two periods to see how $T$ scales with $\sqrt{L}$ .

Intuitive explanation

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