Chapter 11, Problem 70GP

To determine

To Find: The frequency of oscillations.

Explanation of Solution

Given Information:

Height, x = $33\text{cm}$

Mass =m

Formula used:

Simple harmonic motion equation for a spring of mass m is

  $\omega =2\pi f$

  $\omega =\sqrt{\frac{k}{m}}$

Then by using the conservation of energy.

  $E_i=E_f$

Calculation:

  $\begin{array}{l}\frac{1}{2}k{x}^2=mgx\\ \frac{k}{m}=\frac{2g}{x}\end{array}$

For the frequency $f$

  $2\pi f=\sqrt{\frac{k}{m}}$

By using the relation from the above

  $2\pi f=\sqrt{\frac{2g}{x}}$

  $f=\frac{1}{2\pi }\sqrt{\frac{2g}{x}}$

  $f=\frac{1}{2\pi }\sqrt{\frac{2(9.8)}{0.33}}$

  $f=1.22\text{Hz}$

Conclusion:

The frequency of oscillations is $1.22\text{Hz}$ .