If a simple harmonic oscillator has got a displacement of `0.02m` and acceleration equal to `2.0ms^-2` at any time, the angular frequency of the oscillator is equal to

Options

A. `10 rad //s`
B. `0.1 rad//s`
C. `100 rad//s`
D. `1 rad//s`

Answer

To find the angular frequency of a simple harmonic oscillator given its displacement and acceleration, we can follow these steps:

### Step 1: Understand the relationship between acceleration, displacement, and angular frequency
In simple harmonic motion, the acceleration \( a \) is related to the displacement \( x \) and the angular frequency \( \omega \) by the formula:
\[ a = -\omega^2 x \]
For our purposes, we can use the magnitude of acceleration:
\[ |a| = \omega^2 |x| \]

### Step 2: Substitute the known values
We know from the problem that:
- Displacement \( x = 0.02 \, \text{m} \)
- Acceleration \( a = 2.0 \, \text{m/s}^2 \)

Substituting these values into the equation gives:
\[ 2.0 = \omega^2 \cdot 0.02 \]

### Step 3: Solve for \( \omega^2 \)
Rearranging the equation to solve for \( \omega^2 \):
\[ \omega^2 = \frac{2.0}{0.02} \]

### Step 4: Calculate \( \omega^2 \)
Calculating the right-hand side:
\[ \omega^2 = \frac{2.0}{0.02} = 100 \]

### Step 5: Find \( \omega \)
Now, take the square root to find \( \omega \):
\[ \omega = \sqrt{100} = 10 \, \text{radians/second} \]

### Final Answer
The angular frequency of the oscillator is:
\[ \omega = 10 \, \text{radians/second} \]

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