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Question
The pendulum of a clock is replaced by a spring-mass system with the spring having spring constant 0.1 N/m. What mass should be attached to the spring?
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Solution
Given:
Spring constant, k =0.1 N/m
Time period of the pendulum of clock, T = 2 s
Mass attached to the string, m, is to be found.
The relation between time period and spring constant is given as,
\[2 = 2\pi\sqrt{\frac{m}{k}}\]
\[ \Rightarrow \pi^2 \left( \frac{m}{0 . 1} \right) = 1\]
\[ \therefore m = \frac{0 . 1}{\pi^2} = \frac{0 . 1}{10}\]
\[ = 0 . 01 kg \approx 10 g\]
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