Question
In an ideal spring the length is 0.5 kg one of mass vertical oscillations are made by suspending the body. If the oscillation period is $\frac{\pi}{2}$ then what is the spring constant?
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Answer
Given : $m=0.5 kg$ and $T=\frac{\pi}{2} sec$
$T=2 \pi \sqrt{\frac{m}{k}}$
$\frac{\pi}{2}=2 \pi \sqrt{\frac{m}{k}}$
$\frac{1}{4}=\sqrt{\frac{0.5}{k}}$
On squaring
$\frac{1}{16}=\frac{0.5}{k}$
$\begin{aligned} k & =16 \times 0.5 \\ & =8 N / m \end{aligned}$
$T=2 \pi \sqrt{\frac{m}{k}}$
$\frac{\pi}{2}=2 \pi \sqrt{\frac{m}{k}}$
$\frac{1}{4}=\sqrt{\frac{0.5}{k}}$
On squaring
$\frac{1}{16}=\frac{0.5}{k}$
$\begin{aligned} k & =16 \times 0.5 \\ & =8 N / m \end{aligned}$
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