A body of mass 1 kg oscillates on a spring of force constant 16 N/m. Calculate the angular frequency.

Answer

To calculate the angular frequency of a body oscillating on a spring, we can use the formula for angular frequency (\( \omega \)) in simple harmonic motion, which is given by:

\[ \omega = \sqrt{\frac{K}{m}} \]

where:
- \( K \) is the force constant of the spring (in N/m),
- \( m \) is the mass of the body (in kg).

### Step-by-Step Solution:

1. **Identify the given values**:
- Mass of the body, \( m = 1 \, \text{kg} \)
- Force constant of the spring, \( K = 16 \, \text{N/m} \)

2. **Substitute the values into the formula**:
\[ \omega = \sqrt{\frac{K}{m}} = \sqrt{\frac{16 \, \text{N/m}}{1 \, \text{kg}}} \]

3. **Calculate the value inside the square root**:
\[ \frac{16 \, \text{N/m}}{1 \, \text{kg}} = 16 \, \text{s}^{-2} \]

4. **Take the square root**:
\[ \omega = \sqrt{16 \, \text{s}^{-2}} = 4 \, \text{rad/s} \]

5. **State the final answer**:
The angular frequency \( \omega \) of the body oscillating on the spring is:
\[ \omega = 4 \, \text{rad/s} \]