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13.Oscillations
medium
A spring executes $SHM$ with mass of $10\,kg$ attached to it. The force constant of spring is $10\,N/m$.If at any instant its velocity is $40\,cm/sec$, the displacement will be .... $m$ (where amplitude is $0.5\,m$)
A
$0.09$
B
$0.3$
C
$0.03$
D
$0.9$
Solution
(b) Angular velocity $\omega = \sqrt {\left( {\frac{k}{m}} \right)} $$ = \sqrt {\left( {\frac{{10}}{{10}}} \right)} = 1$
Now $u = \omega \sqrt {{a^2} – {y^2}} $
==>${y^2} = {a^2} – \frac{{{u^2}}}{{{\omega ^2}}}$$ = {(0.5)^2} – \frac{{{{(0.4)}^2}}}{{{1^2}}}$
==> ${y^2} = 0.9$
$y = 0.3\,m$
Standard 11
Physics
