Question

The acceleration of a particle is $a=-100x+50.$ It is released from $x=2$ Here $a$ and $x$ are in SI units:

• A. the particle will perform SHM of amplitude $2m$
• B. the particle will perform SHM of amplitude $1.5m$
• C. the particle will perform SHM of time period $0.63s$
• D. the particle will have a maximum velocity of $15m/s$

Answer 1

Answer: (B), (C), (D)

The correct options are
B the particle will perform SHM of time period $0.63s$
C the particle will have a maximum velocity of $15m/s$
D the particle will perform SHM of amplitude $1.5m$

$a=0$ at $x=0.5m$
and particle is released from $x=2m$
Hence,
$A=2-0.5=1.5m$
${\omega }^2=100$
$\therefore \omega =10rad/s$
$T=\frac{2\pi }{\omega }=\frac{2\pi }{10}$
$=0.63s$
$v_{max}=\omega A=\left(10\right)\left(1.5\right)$
$v_{max}=15$ m/s