Chapter 11, Problem 8P

To determine

To find: The value of original mass.

Answer to Problem 8P

The value of original mass is $m=0.6\text{ kg}$ .

Explanation of Solution

Given:

Mass $m\text{ kg}$ .

Additional mass $m+0.680\text{ kg}$ .

Initial frequency ${\nu }_1=0.88\text{ Hz}$ .

Final frequency, ${\nu }_2=0.6\text{ Hz}$ .

Compression in spring, $\text{x = 0}\text{.005m}$ .

Formula used:

Time period of oscillation of spring.

  $T=2\pi \sqrt{\frac{m}{k}}$

Frequency is given by , $\nu =\frac{1}{\text{T}}$ .

Here,

  $m$ is mass on spring,

  $k$ is spring constant,

  $\nu$ is frequency of oscillation,

  $T$ is time period of spring.

Then,

  $\nu \propto \sqrt{\frac{1}{m}}$

Calculation:

From the equation,

  $\nu \propto \sqrt{\frac{1}{m}}$

  $\frac{{\nu }_1}{{\nu }_2}=\sqrt{\frac{m_2}{m_1}}$

Substituting the values

  $\frac{0.88}{0.6}=\sqrt{\frac{0.68+m}{m}}$

Squaring both sides and calculating further,

  $2.15m=m+0.68$

  $m=0.6\text{ kg}$ .

Conclusion:

Thus, the original mass $m=0.6\text{ kg}$ .