Questions: Question 1 (1 points) You want to predict the frequency with which a ball-on-spring system will oscillate. You measure the spring constant to be 106 N / m and use a ball of mass 1.21 kg. What is the linear frequency (in Hz)? Please enter a numerical answer below. Accepted formats are numbers or "e" based scientific notation e.g. 0.23,-2, 1e6, 5.23e-8

Solution Steps

To find the linear frequency of a ball-on-spring system, we use the formula for the angular frequency \(\omega\) of a simple harmonic oscillator:

\[ \omega = \sqrt{\frac{k}{m}} \]

where \(k\) is the spring constant and \(m\) is the mass of the ball.

Given:

• Spring constant, \(k = 106 \, \mathrm{N/m}\)
• Mass of the ball, \(m = 1.21 \, \mathrm{kg}\)

Substitute these values into the formula:

\[ \omega = \sqrt{\frac{106}{1.21}} \]

Calculate \(\omega\):

\[ \omega = \sqrt{87.6033} \approx 9.3565 \, \mathrm{rad/s} \]

The linear frequency \(f\) is related to the angular frequency \(\omega\) by the formula:

\[ f = \frac{\omega}{2\pi} \]

Substitute \(\omega = 9.3565 \, \mathrm{rad/s}\) into the formula:

\[ f = \frac{9.3565}{2\pi} \approx 1.489 \, \mathrm{Hz} \]

Final Answer