A particle having mass 10 g oscillates according to the equation x = (2.0 cm) sin [(100 s^{-1}) t + π/6]. Find (a) the amplitude, the time period and the spring constant (b) the position, the velocity and the acceleration at t = 0.

(a) 2.0 cm, 0.063 s, 100 N m^{-1}

(b) 1.0 cm, 1.73 m^{-1}, 100 m s^{-2}

Given:

The equation of motion of particle executing SHM,

*a).Comparing* *with* *the* *standard* *equation*

We get,

*For* *Spring* *constant,*

*(b).* *Now,* *Given* *Equation,*

*At* *t* *=* *0,*

*Also,* *v* *=* *AωCos(ωt* *+* *Φ)*

*Also,* *a* *=* *-Aω ^{2}Sin(ωt*

1