Chapter 11, Problem 5P

To determine

To calculate: The value of frequency of vibrations.

Answer to Problem 5P

The frequency of vibration is $3.77\text{ Hz}$ .

Explanation of Solution

Given:

Mass $1$ , $M_1\text{ = 0}\text{.6 kg}$ .

Mass $2$ , $M_2\text{ = 0}\text{.38 kg}$ .

Initial frequency $v_1=3\text{ Hz}$ .

Formula used:

Time period of oscillation of spring.

  $T=2\pi \sqrt{\frac{m}{k}}$

Here,

  $T$ is time period of spring,

  $m$ is mass on spring,

  $k$ is spring constant.

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

Then.

  $v\propto \sqrt{\frac{1}{m}}$

Here,

  $\nu$ is frequency of oscillation.

Calculation:

From the equation,

  $v\propto \sqrt{\frac{1}{m}}$

  $\frac{v_1}{v_2}=\sqrt{\frac{m_2}{m_1}}$

Substituting the values

  $\frac{3}{v_2}=\sqrt{\frac{0.38}{0.6}}$

  $v_2=3.77\text{ Hz}$ .

Conclusion:

Thus, the frequency of vibration is $3.77\text{ Hz}$ .