Answer: Option B
:
B
A general sinusoidal, oscillation of amplitude A, angular frequency $\omega andataphase\psi$ is given as
$x\left(t\right)=Asin(\omega t+\psi )$,
Compare this with the equation under discussion
$x=\left[\right(0.2cm\left)sin\right(100s^{-1})t+\frac{\pi }{6}]$
It is clear from a comparison, that
$A=0.2cm=0.002m$
$\omega =100s^{-1},and\psi =\frac{\pi }{6}$
We know that for oscillations in a spring mass system, the spring constant is related to the mass m and ω as
$k=m{\omega }^2$
The mass is given to us, viz. $m=10g=0.01kg$
$\therefore Thek=[0.01\times 1002]kg{s}^{-2}$
$=100kg{s}^{-2}$
Hence correct option is (b).