According to law of conservation of energy, the total energy possessed by the particle should be same everywhere. Let origin be x=0. ∴TE(x=0)=TE(x=a) i.e. PE(x=0)+KE(x=0)=PE(x=a)+KE(x=a)
K(0)2
2
+Ae−α×02+KE(x=0) =Ka22+Ae−αa2+
1
2
mva2 i.e. A+KE(x=0)=
ka2
2
+Ae−αa2+
1
2
mva2 So, A≤
ka2
2
+Ae−αa2+
1
2
mva2[∵KE(x=0). is unknown, A<RHS], if KE(x=0)=0,A=RHS] i.e. A(1−e−αa2)≤