When a particle is performing linear SHM its KE is two times its PE at a position ‘A’ and its PE is two times its KE at another position ‘B’. Find ratio of KEA  to  KEB

At A,        KE=2PE,             ⇒PE=KE/2,                  TE=KE+PE,  substitute,TE=KE+KE2,               ⇒TEA=3KEA2---(1) At B,        PE=2KE,                  TE=KE+PE,  substitute,TE=KE+2KE,               ⇒TEB=3KEB----(2) according to principle of conservation of energy TEA=TEB 3KEA2=3KEB ⇒KEAKEB=21