### Question 15 of 25---**Problem Statement:**What is the mass \( m \) of an object that is attached to a spring with a force constant of 125 N/m if 22 complete oscillations occur each 13 s?---**Answer:**\[ m = \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \]*kg*---**Explanation:**To find the mass \( m \) of the object, given the force constant \( k \) of the spring and the oscillation information, we can use the formula for the period \( T \) of a simple harmonic oscillator:\[ T = 2\pi \sqrt{\frac{m}{k}} \]First, we need to calculate the period \( T \). Given that there are 22 complete oscillations in 13 seconds, we find:\[ T = \frac{13 \, \text{s}}{22} \]Next, we can solve for \( m \) by rearranging the formula:\[ m = \frac{T^2 \cdot k}{4\pi^2} \]By substituting the given values, we can determine the mass \( m \). 1. Calculate the period \( T \): \[ T = \frac{13}{22} \, \text{s} \] 2. Substitute \( T \) and \( k \) into the rearranged formula: \[ m = \frac{\left(\frac{13}{22}\right)^2 \cdot 125}{4\pi^2} \]Finally, simplify the expression to find the mass \( m \).

Name: ### Question 15 of 25---**Problem Statement:**What is the mass \( m \
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: ### Question 15 of 25---**Problem Statement:**What is the mass \( m \) of an object that is attached to a spring with a force constant of 125 N/m if 22 complete oscillations occur each 13 s?---**Answer:**\[ m = \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \