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13.Oscillations
medium
The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If length of spring is cut to one third then the same mass oscillates with frequency $v_2$, then
A
$v_2=3 v_1$
B
$3 v_2=v_1$
C
$v_2=\sqrt{3} v_1$
D
$\sqrt{3} v_2=v_1$
Solution
(c)
$\omega_{\text {old }}=\sqrt{\frac{k_{\text {old }}}{m}}$
When divided into $3$ parts the spring constant of smaller parts
$\therefore k_{\text {final }}=3 k_{\text {old }}$
$\therefore \omega_{\text {linal }}=\sqrt{3} \omega_{\text {old }}$
$\omega=2 \pi v$
Hence $v_{\text {final }}=\sqrt{3} v_{\text {old }} \Rightarrow v_2=\sqrt{3} v_1$
Standard 11
Physics
