Question

A particle having mass 10g oscillates according to the equation $x=\left(2.0cm\right)sin\left[\right(100s^{-1})t+\frac{\pi }{6}]$. Find the spring constant

• A. $200kg/s^2$
• B. $100kg/s^2$
• C. $10,000kg/s^2$
• D. Data insufficient

Answer 1

The correct option is B

$100kg/s^2$

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).