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13.Oscillations
normal
What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless ?
A
$\frac{\pi }{2}\sqrt {\frac{m}{k}}$
B
$\frac{\pi }{2}\sqrt {\frac{m}{2k}}$
C
$\frac{\pi }{2}\sqrt {\frac{2m}{k}}$
D
$\pi \sqrt {\frac{m}{{2k}}}$
Solution
$2 T=m g$
$m g=4 k x_{0}$
$\frac{T}{2}=k x_{0}$
$T=2 k x_{0}$
if displaced
$m g-2 T=m a$
$m g-4 k\left(x_{0}+x\right)=m a$
$\frac{T}{2}=k\left(x_{0}+x\right)$
$T=2 k\left(x_{0}+x\right)$
$T=2 \pi \sqrt{\frac{m}{4 k}}=\pi \sqrt{\frac{m}{k}}$
Standard 11
Physics
