Math Problem Statement
A 2.00 kg mass is connected to a spring with a spring constant of 900 N/m. The displacement is given by the expression x(t) = 12.0 cm sin(ω t). What is the frequency of the simple harmonic motion? Group of answer choices
5.02 Hz
4.21 Hz
3.38 Hz
2.56 Hz
2.05 Hz
Solution
To find the frequency of the simple harmonic motion, we need to analyze the given expression for displacement and relate it to the parameters of simple harmonic motion.
Given information:
- Mass,
- Spring constant,
- Displacement equation:
Step-by-Step Solution:
-
Convert the displacement to meters:
-
Determine the angular frequency, : For a spring-mass system in simple harmonic motion, the angular frequency is given by:
-
Calculate :
-
Convert to frequency : The frequency is related to the angular frequency by: Substituting :
Conclusion:
The correct answer is: 3.38 Hz
Let me know if you want further clarification on any part of the solution!
Here are 5 questions to extend understanding:
- How does mass affect the frequency of simple harmonic motion?
- What would happen to the frequency if the spring constant doubled?
- How would you calculate the period of this motion?
- What role does amplitude play in simple harmonic motion?
- Can you determine the total energy of the system using given parameters?
Tip: For spring-mass systems, increasing mass will decrease the frequency of oscillation because it slows down the system’s response.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Simple Harmonic Motion
Frequency
Angular Frequency
Formulas
ω = √(k/m) (Angular Frequency of Spring-Mass System)
f = ω / (2π) (Frequency from Angular Frequency)
Theorems
Hooke's Law for Springs
Suitable Grade Level
Grades 11-12
Related Recommendation
Simple Harmonic Motion with 3g Mass and Spring Stretching 4cm
Calculate Position of Harmonic Oscillator at 11.2s with SHM Formula
Simple Harmonic Motion of a 55g Object on a Spring: Detailed Solution
Calculate Spring Constant for a Mass-Spring System
Modeling the Position of an Object in Simple Harmonic Motion