WBJEE · Physics · Oscillations
A particle of mass \(m\) is attached to three identical massless springs of spring constant ' \(k\) ' as shown in the figure. The time period of vertical oscillation of the particle is
- A \(2 \pi \sqrt{\frac{m}{k}}\)
- B \(2 \pi \sqrt{\frac{m}{2 k}}\)
- C \(2 \pi \sqrt{\frac{m}{3 k}}\)
- D \(\pi \sqrt{\frac{m}{k}}\)
Answer & Solution
Correct Answer
(B) \(2 \pi \sqrt{\frac{m}{2 k}}\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Hints : } \mathrm{T}=2 \pi \sqrt{\frac{m}{\mathrm{~K}_{\mathrm{eq}}}} \\ & \mathrm{F}=\mathrm{K} x+2 \mathrm{~K} x \cos ^2 45 \\ & \mathrm{~K}_{\mathrm{eq}} x=\mathrm{K} x+\mathrm{K} x \\ & \mathrm{~K}_{\mathrm{eq}}=2 \mathrm{~K} \end{aligned} \]
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