A particle of mass 0.10 kg executes SHM with an amplitude 0.05 m and frequency 20 vib/s. Its energy os oscillation is

Options

A. 2 J
B. 4 J
C. 1 J
D. zero

Explanation

To solve the problem, we need to calculate the energy of a particle executing Simple Harmonic Motion (SHM) using the given parameters: mass (m), amplitude (A), and frequency (f).

### Step-by-step Solution:

1. **Identify the given values:**
- Mass (m) = 0.10 kg
- Amplitude (A) = 0.05 m
- Frequency (f) = 20 vib/s

2. **Calculate the angular frequency (ω):**
The angular frequency (ω) is related to the frequency (f) by the formula:
\[ \omega = 2\pi f \]
Substituting the given frequency:
\[ \omega = 2\pi \times 20 = 40\pi \, \text{rad/s} \]

3. **Use the formula for the total energy (E) in SHM:**
The total energy (E) of a particle in SHM is given by:
\[ E = \frac{1}{2} m \omega^2 A^2 \]

4. **Substitute the values into the energy formula:**
First, calculate \( \omega^2 \):
\[ \omega^2 = (40\pi)^2 = 1600\pi^2 \]
Now substitute \( m \), \( \omega^2 \), and \( A \) into the energy formula:
\[ E = \frac{1}{2} \times 0.10 \times 1600\pi^2 \times (0.05)^2 \]

5. **Calculate \( A^2 \):**
\[ A^2 = (0.05)^2 = 0.0025 \]

6. **Final calculation:**
Now substitute \( A^2 \) into the energy equation:
\[ E = \frac{1}{2} \times 0.10 \times 1600\pi^2 \times 0.0025 \]
\[ E = 0.05 \times 1600\pi^2 \times 0.0025 \]
\[ E = 0.05 \times 4\pi^2 \]
\[ E = 0.20\pi^2 \]

Using \( \pi \approx 3.14 \):
\[ E \approx 0.20 \times (3.14)^2 \approx 0.20 \times 9.8596 \approx 1.97192 \, \text{J} \]

Rounding off, we can say:
\[ E \approx 2 \, \text{J} \]

### Final Answer:
The energy of oscillation is approximately **2 Joules**.

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