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.

Question

Philoid · Accepted Answer

(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),

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 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.