For particle in SHM, the displacement x of the particle as a function o time t is given as x=A sin (2pi t). Here x is in cm and t is in second. Let the time taken by the particle to travel from x=0to x=(A)/(2) be t_(1) and the time taken to travel from x=(A)/(2) to x=A be t_(2) find (t_(1))/(t_(2))

For particle in SHM, the displacement x of the particle as a function

1.	For particle in SHM, the displacement x of the particle as a function o time t is given as x=A sin (2pi t). Here x is in cm and t is in second. Let the time taken by the particle to travel from x=0to x=(A)/(2) be t_(1) and the time taken to travel from x=(A)/(2) to x=A be t_(2) find (t_(1))/(t_(2))
Answer» SOLUTION :Here x=0 at t=0 Also `omega =(2pi)/(T)= 2pi, "":. T=1s` At `t=t_(1), x=(A)/(2)` `(A)/(2)=A sin (2pi t_(1))` (or) `(1)/(2)= sin (2pi t_(1))` `:. 2pi t_(1)=(pi)/(6) (or) t_(1)=(1)/(12) s` TIME taken from x =0 to `x=A` is `(T)/(4)=(1)/(4)s` (or) `t_(1)+t_(2)=(T)/(2)=(1)/(4)s` Hence `(t_(1))/(t_(2))=(1//12)/(1//6)=(1)/(2)`