Acceleration-displacement graph of a particle executing SHM is as shown in the figure. The time period of oscillation is (in sec)

$2 π$
$\frac{π}{2}$
$π$
$\frac{π}{4}$

Question

Acceleration-displacement graph of a particle executing SHM is as shown in the figure- The time period of oscillation is -in sec- 2pi  dfrac-pi-2-  pi  dfrac-pi-4-

Toppr Admin · Accepted Answer

In SHMa-x2212-x3C9-2xora-x2212-Kmxso- from graph-x2212-Km-x2212-1 -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -x2235-slope-xA0-is-xA0-x2212-1-Km-1Time period -2-x3C0-x221A-mK-2-x3C0-x221A-11-2-x3C0-

Acceleration-displacement graph of a particle executing SHM is as shown in the figure. The time period of oscillation is (in sec)2ππ2ππ4

In SHMa=−ω2xora=−Kmxso, from graph−Km=−1 (∵slope is −1)Km=1Time period =2π√mK=2π√11=2π

Acceleration-displacement graph of a particle executing SHM is as shown in the figure. The time period of oscillation is (in sec)

$2 π$
$\frac{π}{2}$
$π$
$\frac{π}{4}$

In SHM
$a = - ω^{2} x$
or
$a = \frac{- K}{m} x$
so, from graph
$- \frac{K}{m} = - 1$ $(∵ s l o p e i s - 1)$
$\frac{K}{m} = 1$
Time period $= 2 π \sqrt{\frac{m}{K}}$
$= 2 π \sqrt{\frac{1}{1}}$
$= 2 π$