Problem 61
Question
A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation in the form \(d=\sin \omega t\) for the simple harmonic motion.
Step-by-Step Solution
Verified Answer
The equation for the simple harmonic motion using the given data is \(d=\sin(2 \pi \times 264 \cdot t)\).
1Step 1: Analyze the given data
The frequency, denoted by 'f', is given as 264 vibrations per second.
2Step 2: Calculate the Angular Frequency
Angular frequency, denoted by '\(\omega\)', can be calculated using the formula \(\omega = 2 \pi f\). Substituting the value of 'f', we get \(\omega = 2 \pi \times 264\).
3Step 3: Write the equation for simple harmonic motion
With calculated '\(\omega\)', it's possible to write the simple harmonic motion equation as \(d=\sin \omega t\).
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