Spring Block System: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Spring Block System. Understanding the underlying formula is key to arriving at the correct answer below:

For two springs connected in series, the equivalent spring constant is $ k_{eq} = \frac{k_1k_2}{k_1 + k_2} $. Substituting this into the time period formula $ T = 2\pi \sqrt{\frac{m}{k_{eq}}} $ yields $ T = 2\pi \sqrt{\frac{m(k_1 + k_2)}{k_1k_2}} $.