Question

In the given figure, the block is displaced slightly and released. Then, the time period of oscillation is:

• A. $T=2\pi \sqrt{\frac{2m}{K}}$
• B. $T=2\pi \sqrt{\frac{m}{K}}$
• C. $T=2\pi \sqrt{\frac{m}{2K}}$
• D. $T=2\pi \sqrt{\frac{m}{3K}}$

Answer 1

The correct option is C $T=2\pi \sqrt{\frac{m}{2K}}$

If we displace the block on either side of the mean position, we observe that the displacement of each spring is the same. So, it's a parallel combination.



In a parallel combination, the equivalent spring constant is given by,
$K_{\text{eq}}=K_1+K_2=2K$
Then,
Time period of oscillation
$T=2\pi \sqrt{\frac{m}{K_{eq}}}=2\pi \sqrt{\frac{m}{2K}}$
Thus, option (c) is the correct answer.