More practice questions

4. Q4. The square of a pendulum’s amplitude falls to a quarter of its starting value. What has happened to the amplitude and to the energy?

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   The energy is proportional to A^², so it has also fallen to a quarter. The amplitude has fallen to √¼ = ½ of its starting value.

5. Q5. In the data of Example 2, A^² falls to about 0.79 of its value every 40 s. Starting from 100 cm^², what would you expect after 80 s?

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   100 × 0.79 × 0.79, about 62.4 cm^², which matches the reading at 80 s.

6. Q6. A student plots L against T^² for several lengths and gets a straight line of slope 0.25 m s^⁻². Find g.

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   L = (g/4π^²)T^², so the slope is g/4π^². Then g = 4π^² × 0.25, about 9.87 m s^⁻². (With g = 9.8 m s^⁻² the slope would be 0.248 m s^⁻².)