hi guys
here's another problem
a particle is executing S.H.M in a straight line. in first second starting from rest it covers a distance a and next second distance b in same direction. find out the amplitude.
Let the equation of SHM be x = Acos wt
In 1st second distance travelled = a = Acos w, => cos w=a/A ----- (1)
In 2 seconds distance travelled = d(say) = Acos 2w
=> b = d-a = A(cos 2w - cos w) =A(2cos2w - 1 -cos w)
=>b=A[2(a/A)2 -(a/A) - 1] => A2 + (a+b)A - 2a2=0
or Amplitude = A = -(a+b) + {(a+b)2 + 8a2 }1/2
2