The damping force on an oscillator is directly proportional to the velocity. The units of the constant to proportionality are

Options

A. `kg ms^(-1)`
B. `kg ms^(-2)`
C. `kg s^(-1)`
D. `kg s`

Answer

To find the units of the constant of proportionality in the damping force equation, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The damping force \( F \) on an oscillator is given by the equation:
\[ F = k \cdot v \]
where \( k \) is the constant of proportionality and \( v \) is the velocity.

2. **Identifying Units**:
- The unit of force \( F \) is Newton (N), which can be expressed in base units as:
\[ 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \]
- The unit of velocity \( v \) is meters per second (m/s).

3. **Rearranging the Equation**:
To find the units of the constant \( k \), we can rearrange the equation:
\[ k = \frac{F}{v} \]

4. **Substituting Units**:
Now, substituting the units of force and velocity into the equation for \( k \):
\[ k = \frac{\text{kg} \cdot \text{m/s}^2}{\text{m/s}} \]

5. **Simplifying the Units**:
When we simplify the units:
\[ k = \frac{\text{kg} \cdot \text{m/s}^2}{\text{m/s}} = \frac{\text{kg} \cdot \text{m}}{\text{s}^2} \cdot \frac{\text{s}}{\text{m}} = \frac{\text{kg}}{\text{s}} \]

6. **Final Result**:
Thus, the units of the constant of proportionality \( k \) are:
\[ \text{kg/s} \]

### Summary:
The units of the constant of proportionality in the damping force equation are \( \text{kg/s} \).