Write the displacement equation representing the following conditions obtained for a simple harmonic motion: amplitude=0.01m, frequency=600Hz initial phase `=pi//6`

Answer

To derive the displacement equation for the given conditions of simple harmonic motion (SHM), we will follow these steps:

### Step 1: Identify the standard equation of SHM
The standard equation for the displacement \( Y \) in simple harmonic motion is given by:
\[ Y = A \sin(\omega t + \phi) \]
where:
- \( Y \) is the displacement,
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( t \) is the time,
- \( \phi \) is the initial phase.

### Step 2: Substitute the given amplitude
From the problem, we know that the amplitude \( A \) is given as:
\[ A = 0.01 \, \text{m} \]

### Step 3: Calculate the angular frequency \( \omega \)
The angular frequency \( \omega \) can be calculated using the formula:
\[ \omega = 2\pi f \]
Given that the frequency \( f \) is \( 600 \, \text{Hz} \), we can substitute this value into the equation:
\[ \omega = 2\pi \times 600 \]
Calculating this gives:
\[ \omega = 1200\pi \, \text{radians/second} \]

### Step 4: Substitute the initial phase
The initial phase \( \phi \) is given as:
\[ \phi = \frac{\pi}{6} \]

### Step 5: Write the complete displacement equation
Now, substituting the values of \( A \), \( \omega \), and \( \phi \) into the standard equation:
\[ Y = 0.01 \sin(1200\pi t + \frac{\pi}{6}) \]

### Final Displacement Equation
Thus, the displacement equation representing the given conditions for simple harmonic motion is:
\[ Y = 0.01 \sin(1200\pi t + \frac{\pi}{6}) \]

---