If the period of oscillation of mass M suspended. From a spring is one second, then the period of 4 M will be

Options

A. `1//2`
B. `1//4` sec
C. 2 sec
D. 4 sec

Explanation

To solve the problem, we need to understand the relationship between the mass suspended from a spring and the period of oscillation. The formula for the period of oscillation \( T \) of a mass \( m \) suspended from a spring with spring constant \( k \) is given by:

\[ T = 2\pi \sqrt{\frac{m}{k}} \]

### Step-by-Step Solution:

1. **Identify the given information**:
- The period of oscillation for mass \( m \) is given as \( T = 1 \) second.

2. **Write the formula for the period**:
- For mass \( m \):
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
- Since we know \( T = 1 \) second, we can write:
\[ 1 = 2\pi \sqrt{\frac{m}{k}} \]

3. **Calculate the period for mass \( 4m \)**:
- Now, we need to find the period when the mass is \( 4m \):
\[ T' = 2\pi \sqrt{\frac{4m}{k}} \]

4. **Simplify the expression**:
- We can factor out the square root:
\[ T' = 2\pi \sqrt{4} \sqrt{\frac{m}{k}} = 2\pi \cdot 2 \sqrt{\frac{m}{k}} = 4\pi \sqrt{\frac{m}{k}} \]

5. **Relate it to the original period**:
- From the original period \( T = 2\pi \sqrt{\frac{m}{k}} = 1 \) second, we can substitute:
\[ T' = 4 \cdot \frac{1}{2} = 2 \text{ seconds} \]

6. **Conclusion**:
- Therefore, the period of oscillation for mass \( 4m \) is \( T' = 2 \) seconds.

### Final Answer:
The period of oscillation of mass \( 4M \) will be **2 seconds**.