The mechanical energy of a system is given by E = A x 2 + B v 2 where x is the displacement from ( x = 0 ) and v is the velocity of the body at x then choose the CORRECT statement(s). Assume A and B p

Question

The mechanical energy of a system is given by E = A x 2 + B v 2 where x is the displacement from ( x = 0 ) and v is the velocity of the body at x then choose the CORRECT statement(s). Assume A and B positive constant and total mechanical energy of the system remains constant.

TestHub · Accepted Answer

Ans. (A,B,C,D) At max. amp. v = 0 ; E = Ax 2 ⇒ x = A E ​ ​ For man vel. x = 0 ; E = B v 2 ⇒ v = B E ​ ​ U = Ax 2 F = − ∂ x ∂ v ​ = − 2 Ax ⇒ F ( at x = 0 ) = 0 ∴ x = 0 is eq. position. ​ F = − 2 A x ⇒ a = m − 2 A x ​ ​ 2 1 ​ m v 2 = B v 2 ⇒ m = 2 B ​ ∴ a = − B A ​ x ​

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