Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time t = 0. amplitude 2.4 m, frequency 800 Hz
Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time t = 0. amplitude 2.4 m, frequency 800 Hz
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time
t = 0.
amplitude 2.4 m, frequency 800 Hz
y = _________
![**Simple Harmonic Motion Problem**
*Objective:*
Find a function that models the simple harmonic motion with the given properties. Assume that the displacement is at its maximum at time \( t = 0 \).
*Given:*
- Amplitude: \( 2.4 \, \text{m} \)
- Frequency: \( 800 \, \text{Hz} \)
*Solution:*
The function proposed is:
\[
y = 2.4 \sin (1600\pi t)
\]
*Notes:*
- The box around the function and the red "X" implies an error in the proposed solution.
- In harmonic motion, the standard form is typically \( y = A \sin (2\pi ft) \) or \( y = A \sin (\omega t) \), where \( \omega \) (angular frequency) is \( 2\pi \times \) frequency.
- Here, the angular frequency should have been calculated as \( 2\pi \times 800 = 1600\pi \), making \( 1600\pi \) correct in this context. However, the "X" indicates there might be another aspect that needs attention for a fully correct solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50b7307d-f147-4c39-812e-01e48cbfa721%2Fabdef8b9-3ba7-422b-93ac-1c5aa6455222%2Fo0svc5_processed.png&w=3840&q=75)
Transcribed Image Text:**Simple Harmonic Motion Problem**
*Objective:*
Find a function that models the simple harmonic motion with the given properties. Assume that the displacement is at its maximum at time \( t = 0 \).
*Given:*
- Amplitude: \( 2.4 \, \text{m} \)
- Frequency: \( 800 \, \text{Hz} \)
*Solution:*
The function proposed is:
\[
y = 2.4 \sin (1600\pi t)
\]
*Notes:*
- The box around the function and the red "X" implies an error in the proposed solution.
- In harmonic motion, the standard form is typically \( y = A \sin (2\pi ft) \) or \( y = A \sin (\omega t) \), where \( \omega \) (angular frequency) is \( 2\pi \times \) frequency.
- Here, the angular frequency should have been calculated as \( 2\pi \times 800 = 1600\pi \), making \( 1600\pi \) correct in this context. However, the "X" indicates there might be another aspect that needs attention for a fully correct solution.
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