Chapter 11, Problem 80GP

To determine

To find: The maximum amplitude of the oscillation.

Answer to Problem 80GP

The maximum amplitude of the oscillations is $0.110\text{m}$ .

Explanation of Solution

Given:

Frequency of oscillation $f=1.5\text{Hz}$

  $g=9.8$

Concept used:

The maximum amplitude of the oscillation is

  $\begin{array}{l}m{a}_{\max }=kA\\ a_{\max }=\frac{kA}{m}={\omega }^{2}A=4{\pi }^2{f}^{2}A\\ a_{\max }=4{\pi }^2{f}^{2}A\ge g\\ a\le \frac{g}{4{\pi }^2{f}^{2}A}\end{array}$

Calculation:

Substituting the values,

  $a\le \frac{9.8}{4{\pi }^2{(1.5)}^2}$

  $a\le 0.110\text{m}$

Conclusion:

The maximum amplitude of the oscillations is $0.110\text{m}$ so that the pebble placed on the road does not lose contact.