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

To find the length of the pendulum, we can use the formula for the period of a simple pendulum:<br /><br />$T = 2\pi\sqrt{\frac{L}{g}}$<br /><br />where $T$ is the period, $L$ is the length of the pendulum, and $g$ is the acceleration due to gravity.<br /><br />Given that the frequency of the pendulum is 0.19 Hz, we can find the period by taking the reciprocal of the frequency:<br /><br />$T = \frac{1}{f} = \frac{1}{0.19} \approx 5.26$ seconds<br /><br />Now we can substitute the values of $T$ and $g$ into the formula and solve for $L$:<br /><br />$5.26 = 2\pi\sqrt{\frac{L}{9.81}}$<br /><br />Dividing both sides by $2\pi$, we get:<br /><br />$\frac{5.26}{2\pi} = \sqrt{\frac{L}{9.81}}$<br /><br />Squaring both sides, we have:<br /><br />$\left(\frac{5.26}{2\pi}\right)^2 = \frac{L}{9.81}$<br /><br />Multiplying both sides by $9.81$, we get:<br /><br />$L = \left(\frac{5.26}{2\pi}\right)^2 \times 9.81 \approx 8.06$ meters<br /><br />Therefore, the length of the pendulum is approximately 8.06 meters.