Sum

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,

\[T = 2\pi \sqrt{\left( \frac{m}{k} \right)}\]

On substituting the respective values, we get:

\[2 = 2\pi\sqrt{\frac{m}{k}}\]

\[ \Rightarrow \pi^2 \left( \frac{m}{0 . 1} \right) = 1\]

\[ \therefore m = \frac{0 . 1}{\pi^2} = \frac{0 . 1}{10}\]

\[ = 0 . 01 kg \approx 10 g\]

Concept: Energy in Simple Harmonic Motion

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