A particle moves with a simple harmonic motion 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 in the same direction. The amplitude of the motion is

Let the acceleration be f; f=−ω2xTherefore, distance of the particle from the centre at any time t is given by x=rcos⁡(ωt) where r is the amplitude when t=1s,x=r−a∴ (r−a)=rcos⁡ωcos⁡ω=r−ar     ........(i) When t=2s,x=r−a−b, therefore  r−a−b=cos⁡2ω∴ r−a−b=r2cos2⁡ω−1    ………..(ii)Substituting the value of cos⁡ω from Eq. (i) in Eq. (ii), we get r−a−b=r2(r−a)2r2−1=2(r−a)2r−r∴ r(3a−b)=2a2⇒r=2a23a−b