Maximum K.E. of a mass of 1 kg executing SHM is18 J . Amplitude of motion is6 cm , its angular frequency is

Options

A. `25 rad s^(-1)`
B. ` 50 rad s^(-1)`
C. ` 75 rad s^(-1)`
D. ` 100 rad s^(-1)`

Answer

To find the angular frequency (ω) of a mass executing simple harmonic motion (SHM) given its maximum kinetic energy (K.E.) and amplitude, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Mass (m) = 1 kg
- Maximum Kinetic Energy (K.E.) = 18 J
- Amplitude (A) = 6 cm = 0.06 m (convert cm to m)

2. **Use the Formula for Maximum Kinetic Energy:**
The maximum kinetic energy in SHM is given by the formula:
\[ K.E. = \frac{1}{2} m \omega^2 A^2 \]
where:
- \( K.E. \) is the maximum kinetic energy,
- \( m \) is the mass,
- \( \omega \) is the angular frequency,
- \( A \) is the amplitude.

3. **Substitute the Known Values into the Equation:**
\[ 18 = \frac{1}{2} \times 1 \times \omega^2 \times (0.06)^2 \]

4. **Simplify the Equation:**
\[ 18 = \frac{1}{2} \times \omega^2 \times 0.0036 \]
\[ 18 = 0.0018 \omega^2 \]

5. **Solve for \( \omega^2 \):**
\[ \omega^2 = \frac{18}{0.0018} \]
\[ \omega^2 = 10000 \]

6. **Take the Square Root to Find \( \omega \):**
\[ \omega = \sqrt{10000} = 100 \text{ radians/second} \]

### Final Answer:
The angular frequency \( \omega \) is **100 radians/second**.