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
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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.
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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