A particle performs SHM in a straight line. In the first second starting from rest, it travels a distance a and in the next second, it travels a distance b on the same side of mean position. The amplitude of the SHM is

Particle starts from rest. Hence, x=A cos ωt                                   a=A-x=A-Acos(ω×1)or                          cos ω=A-aA=1-aA⇒                        a + b=A - A cos (ω×2)                                       =A-A(2 cos2 ω - 1)                                        =2A-2A1-aA2On solving, we get                                      A=2a23a-b