For a particle in SHM, the displacement x of the particle as a function of time t is given as x=A (2 t) . Here x is in cm and t is in seconds. Let the time taken by the particle to travel from x=0 to x=A / 2 be t₁ and the time taken to travel from x=A / 2 to x=A be t₂ . Find t₁ / t₂ .

Step-by-step solution

Here x=0 at t=0 . Also =2 / T=2 T=1 ~s At t=t₁, x= A / 2 . Therefore, aligned & A 2 =A (2 t₁ ) or 1 2 = (2 t₁ ) & 2 t₁= 6 or t₁= 1 12 ~s aligned Time taken from x=0 to x=A is T 4 = 1 4 ~s or t₁+t₂= T 4 = 1 4 ~s or t₂= 1 4 - 1 12 = 1 6 ~s Hence, t₁ t₂ = 1 / 12 1 / 6 = 1 2 .