Bradley Vargas
04/21/2024 · Primary School
11) Discussion Topic: 1. A mass-spring system has a mass ( m ) of 0.5 kg and a stiffness \( (\mathrm{k}) \) of \( 100 \mathrm{~N} / \mathrm{m} \). Calculate the natural frequency ( \( \omega \mathrm{n}) \) of the system.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
The natural frequency \( \omega_n \) of a mass-spring system can be calculated using the formula:
\[
\omega_n = \sqrt{\frac{k}{m}}
\]
where:
- \( k \) is the stiffness of the spring (in N/m),
- \( m \) is the mass (in kg).
Given:
- \( m = 0.5 \, \text{kg} \)
- \( k = 100 \, \text{N/m} \)
Now, substituting the values into the formula:
\[
\omega_n = \sqrt{\frac{100 \, \text{N/m}}{0.5 \, \text{kg}}}
\]
Calculating the fraction:
\[
\frac{100}{0.5} = 200
\]
Now, taking the square root:
\[
\omega_n = \sqrt{200} \approx 14.14 \, \text{rad/s}
\]
Thus, the natural frequency of the system is approximately \( 14.14 \, \text{rad/s} \).
Quick Answer
The natural frequency \( \omega_n \) is approximately \( 14.14 \, \text{rad/s} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
(0)
Ask Real Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
PREV 
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
