A spring mass system oscillates in a car. If the car accelerates on a horizontal road, the frequency of oscillation will

Options

A. increases
B. decreases
C. remain same
D. become zero

Answer

To solve the question regarding the behavior of a spring-mass system oscillating in an accelerating car, we can follow these steps:

### Step 1: Understand the Frequency of Oscillation
The frequency of oscillation \( f \) of a spring-mass system is given by the formula:
\[ f = \frac{1}{T} \]
where \( T \) is the time period of oscillation.

### Step 2: Determine the Time Period
The time period \( T \) of a spring-mass system is given by:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where \( m \) is the mass attached to the spring and \( k \) is the spring constant.

### Step 3: Substitute Time Period into Frequency Formula
Substituting the expression for \( T \) into the frequency formula, we get:
\[ f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \]

### Step 4: Analyze the Dependence of Frequency on Variables
From the equation \( f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \), we can see that the frequency \( f \) depends only on the spring constant \( k \) and the mass \( m \).

### Step 5: Consider the Effect of Car Acceleration
When the car accelerates, it does not change the spring constant \( k \) or the mass \( m \) of the spring-mass system. The acceleration of the car does not influence the oscillation frequency of the spring-mass system.

### Step 6: Conclusion
Since the frequency \( f \) does not depend on the acceleration of the car, we conclude that the frequency of oscillation will remain the same.

Thus, the correct answer is that the frequency of oscillation will **remain the same**.

### Final Answer:
The frequency of oscillation will remain the same (Option 3).

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