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 = -Aω2Sin(ωt + Φ),





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