Question

Two springs of force constants \( k_1 \) and \( k_2 \) are connected to a mass \( m \) as shown. The angular frequency of this configuration is:

• A. \( \frac{k_1 + k_2}{m} \)
• B. \( \sqrt{\frac{k_1 + k_2}{m}} \)
• C. \( \sqrt{\frac{k_1}{k_2 m}} \)
• D. \( \frac{k_2 m}{k_1} \)

Hint:

For parallel spring-mass systems, add the spring constants: \( k_{\text{eff}} = k_1 + k_2 \) and use \( \omega = \sqrt{\frac{k_{\text{eff}}}{m}} \)

Answer 1

The Correct Option is B

In the figure, both springs are connected to a single mass \( m \) from opposite ends. This is a case of parallel spring configuration. When two springs are attached in this way: - The effective spring constant is: \[ k_{\text{eff}} = k_1 + k_2 \] For a spring-mass system, the angular frequency \( \omega \) is given by: \[ \omega = \sqrt{\frac{k_{\text{eff}}}{m}} = \sqrt{\frac{k_1 + k_2}{m}} \] Hence, the angular frequency is: \[ \boxed{\omega = \sqrt{\frac{k_1 + k_2}{m}}} \]