SHMMedium
Question
A particle is performing S.H.M with acceleration a = 8π2 - 4π2 x where x is coordinate of the particle w.r.t the origin. The parameters are in S.I units. The particle is at rest at x = - 2 at t = 0.
Options
A.coordinate of the particle w.r.t origin at any time t is 2 - 4 cos2πt
B.coordinate of the particle w.r.t origin at any time t is - 2 + 4 cos2πt
C.coordinate of the particle w.r.t origin at any time t is - 4 + 2 cos2πt
D.the coordinate cannot be found because mass of the particle is not given.
Solution
a = 8π2 - 4π2 = -4π2(x - 2) ⇒ ω = 2π
Here a = 0 so mean position at x = 2
Let x = A sin (ωt + φ)
As particle is at rest at x = - 2(extreme position and) Amplitude = 4as particle start from extreme position. Therefore
x - 2 = - 4 cos 2πt ⇒ x = 2 - 4 cos 2πt
Here a = 0 so mean position at x = 2
Let x = A sin (ωt + φ)
As particle is at rest at x = - 2(extreme position and) Amplitude = 4as particle start from extreme position. Therefore
x - 2 = - 4 cos 2πt ⇒ x = 2 - 4 cos 2πt
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