Question

As shown in figure a simple harmonic motion oscillator having identical four springs has time period

• A. $T=2\pi \sqrt{\frac{m}{4k}}$
• B. $T=2\pi \sqrt{\frac{m}{2k}}$
• C. $T=2\pi \sqrt{\frac{m}{k}}$
• D. $T=2\pi \sqrt{\frac{m}{8k}}$

Answer 1

Answer: (C)

$T=2\pi \sqrt{\frac{m}{k}}$

Answer 2

$k_{1}$ and $k_{2}$ are parallel and $k_{3}$ and $k_{4}$ are parallel. The two combinations are in series with each other $k_{1}+k_{2} =2 k$ $k_{3}+k_{4} =4 k$ $\frac{1}{k_{ eq }} =\frac{1}{2 k}+\frac{1}{2 k}$ $k_{ eq } =k$ $T =2 \pi \sqrt{\frac{m}{k}}$