The Pendulum of a Clock is Replaced by a Spring-mass System with the Spring Having Spring Constant 0.1 N M−1. What Mass Should Be Attached to the Spring? - Physics

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?

Solution

Given:
Spring constant, =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:

$2 = 2\pi\sqrt{\frac{m}{k}}$

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

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

$= 0 . 01 kg \approx 10 g$

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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 12 Simple Harmonics Motion
Q 9 | Page 252