Chapter 11, Problem 3P

To determine

To find: The value of frequency of vibrations.

Answer to Problem 3P

The frequency of vibration is $\text{1}\text{.482 Hz}$ .

Explanation of Solution

Given:

Mass of the Car, ${\text{W}}_c\text{ = 1500 kg}$ .

Mass of the driver, ${\text{W}}_d\text{ = 68 kg}$ .

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

Formula used:

• Restoring force of spring

  $F=-kx$

Here,

  $k$ is spring constant,

  $F$ is spring restoring force,

  $x$ is displacement of spring.

• Time period of oscillation of spring.

  $T=2\pi \sqrt{\frac{m}{k}}$

Here,

  $m$ is mass on spring,

  $k$ is spring constant.

• Frequency is given by,

  $v=\frac{1}{T}$

Here,

  $\nu$ is frequency of oscillation,

  $T$ is time period of spring.

Calculation:

Substituting the values

  $\frac{F}{x}=k$

  $k=\frac{\text{68}\times 10}{0.005}$ = $136000\text{ N/m}$

Now using

  $T=2\pi \sqrt{\frac{m}{k}}$

  $\begin{array}{l}T=2\pi \sqrt{\frac{1568}{136000}}\\ =2\pi \times 0.107375\\ =0.6747\text{s}\end{array}$

  $\begin{array}{l}v=\frac{1}{\text{T}}\\ =\frac{1}{0.6747}\\ =1.482\text{Hz}\end{array}$

  $v=\text{ 1}\text{.482 Hz}$ .

Conclusion:

Thus, the frequency of vibration is $\text{1}\text{.482 Hz}$ .