If the displacement- velocity and acceleration of particle in SHM are 1 cm-1 cm-sec and 1 cm-sec-2- respectively its time period -in secs- will be-pi0-5 pi2 pi1-5 pi

Question

Toppr Admin · Accepted Answer

X-1cmv-1cm-sa-1cm-sWe know that a-x2212-w2x-x21D2-a-w2-x-x21D2-w2-a-x-1cm-s21cm-11s2-x21D2-w-1rad-stime period T-2-x3C0-w-2-x3C0-1-2-x3C0-sec-xA0-

If the displacement, velocity and acceleration of particle in $S H M$ are $1 c m, 1 c m / s e c$ and $1 c m / s e c^{2}$ respectively its time period (in secs) will be:
$π$
$0.5 π$
$2 π$
$1.5 π$

$x = 1 c m$
$v = 1 c m / s$
$a = 1 c m / s$
We know that $a = - w^{2} x$
$\Rightarrow | a | = w^{2} | x |$
$\Rightarrow w^{2} = \frac{| a |}{| x |} = \frac{1 c m / s^{2}}{1 c m} = 1 \frac{1}{s^{2}}$
$\Rightarrow w = 1 r a d / s$
time period $T = \frac{2 π}{w} = \frac{2 π}{1} = 2 π s e c$

If the displacement, velocity and acceleration of particle in SHM are 1 cm,1 cm/sec and 1 cm/sec2 respectively its time period (in secs) will be:π0.5 π2 π1.5 π

x=1cmv=1cm/sa=1cm/sWe know that a=−w2x⇒|a|=w2|x|⇒w2=|a||x|=1cm/s21cm=11s2⇒w=1rad/stime period T=2πw=2π1=2πsec

If the displacement, velocity and acceleration of particle in $S H M$ are $1 c m, 1 c m / s e c$ and $1 c m / s e c^{2}$ respectively its time period (in secs) will be:
$π$
$0.5 π$
$2 π$
$1.5 π$

$x = 1 c m$
$v = 1 c m / s$
$a = 1 c m / s$
We know that $a = - w^{2} x$
$\Rightarrow | a | = w^{2} | x |$
$\Rightarrow w^{2} = \frac{| a |}{| x |} = \frac{1 c m / s^{2}}{1 c m} = 1 \frac{1}{s^{2}}$
$\Rightarrow w = 1 r a d / s$
time period $T = \frac{2 π}{w} = \frac{2 π}{1} = 2 π s e c$