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

Options

A. 1/2 s
B. 1/4 s
C. 2 s
D. 4s

Explanation

To solve the problem, we need to understand the relationship between the mass attached to a spring and the period of oscillation.

### Step-by-Step Solution:

1. **Understand the Formula for Period of Oscillation**:
The period \( T \) of a mass \( m \) attached to a spring is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where \( k \) is the spring constant.

2. **Identify Given Information**:
We are given that the period of oscillation for mass \( M \) is \( T = 1 \) second.

3. **Determine the Period for Mass \( 4M \)**:
Now, we need to find the period when the mass is increased to \( 4M \). Plugging \( 4M \) into the formula, we have:
\[ T' = 2\pi \sqrt{\frac{4M}{k}} \]

4. **Simplify the Expression**:
We can simplify this expression:
\[ T' = 2\pi \sqrt{\frac{4M}{k}} = 2\pi \cdot 2 \sqrt{\frac{M}{k}} = 2 \cdot (2\pi \sqrt{\frac{M}{k}}) = 2T \]
Since we know \( T = 1 \) second, we can substitute:
\[ T' = 2 \cdot 1 = 2 \text{ seconds} \]

5. **Conclusion**:
Therefore, the period of oscillation for mass \( 4M \) is \( 2 \) seconds.

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