+0

# Physics

0
163
1

Find the length of a pendulum that oscillates with a frequency of 0.19 Hz. The acceleration due to gravity is 9.81 m/s 2 .

Guest Apr 3, 2017
Sort:

### 1+0 Answers

#1
+18626
+3

Find the length of a pendulum that oscillates with a frequency of 0.19 Hz.

The acceleration due to gravity is 9.81 m/s 2 .

Formula:

For small amplitudes, the period of such a pendulum can be approximated by:

$$\begin{array}{|lrcll|} \hline & T &=& 2\pi\sqrt{\frac{L}{g}} \\ \qquad L~ \text{expresses the pendulum length in meters } \\ \qquad g~ \text{expresses the acceleration of gravity}\approx 9.81 \frac{m}{s^2} \\ & T &=& \frac{1}{f} \\ \qquad f~ \text{expresses the frequency in Hz} \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline \frac{1}{f} &=& 2\pi\sqrt{\frac{L}{g}} \\ \frac{1}{2\pi f} &=& \sqrt{\frac{L}{g}} \\ \Big(\frac{1}{2\pi f}\Big)^2 &=& \frac{L}{g} \\ L &=& g\cdot \Big(\frac{1}{2\pi f}\Big)^2 \\ L &=& 9.81\cdot \left(\frac{1}{2\pi\cdot 0.19}\right)^2 \\ L &=& 9.81\cdot \left(0.83765759522\right)^2 \\ L &=& 9.81\cdot 0.70167024683 \\ \mathbf{L} &\mathbf{=}& \mathbf{6.88338512141\ m} \\ \hline \end{array}$$

The length of the pendulum is 6.88 m

heureka  Apr 3, 2017

### 13 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details