BdPhO Regional (Dhaka-South) Secondary 2019/3
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A spring of spring constant $k$ with a mass m attached to it has a resonant frequency $f$. If the mass is doubled and the spring constant is changed to $4k$, then express the new resonant frequency $f_n$ in terms of $f$.
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Re: BdPhO Regional (Dhaka-South) Secondary 2019/3
We know, $T=2\pi\sqrt{\dfrac{m}{k}}$
So, $T_n=2\pi\sqrt{\dfrac{2m}{4k}}=\dfrac{1}{\sqrt2}2\pi\sqrt{\dfrac{m}{k}}$
$\therefore \dfrac{f_n}{f}=\dfrac{T}{T_n}=$$\sqrt2$
So, $T_n=2\pi\sqrt{\dfrac{2m}{4k}}=\dfrac{1}{\sqrt2}2\pi\sqrt{\dfrac{m}{k}}$
$\therefore \dfrac{f_n}{f}=\dfrac{T}{T_n}=$$\sqrt2$
$The$ $only$ $way$ $to$ $learn$ $mathematics$ $is$ $to$ $do$ $mathematics$. $-$ $PAUL$ $HALMOS$