Question

Two identical springs of spring constant ${}^{\prime }2k^{\prime }$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. Then, time period of oscillations of this system is:

• A. $\pi \sqrt{\frac{m}{k}}$
• B. $\pi \sqrt{\frac{m}{2k}}$
• C. $2\pi \sqrt{\frac{m}{k}}$
• D. $2\pi \sqrt{\frac{m}{2k}}$

Answer 1

The correct option is A $\pi \sqrt{\frac{m}{k}}$


Springs are in parallel combination.
Hence, $k_{\text{eff}}=2k+2k=4k$
$\because T=2\pi \sqrt{\frac{m}{k_{\text{eff}}}}$
$T=2\pi \sqrt{\frac{m}{4k}}=\pi \sqrt{\frac{m}{k}}$