Question

A boy is executing simple Harmonic Motion. At a displacement x its potential energy is E₁ and at a displacement y its potential energy is E₂. The potential energy E at displacement (x + y) is(a) $\sqrt{E}=\sqrt{E_{1}}-\sqrt{E_{2}}$(b) $\sqrt{E}=\sqrt{E_{1}}+\sqrt{E_{2}}$(c) E = E₁ + E₂(d) E = E₁ - E₂

Answer 1

stop working Robert do so do

Answer 2

Answer:

√E = √E₁ +√E₂

Explanation:

Potential energy at displacement x = E₁ (Given)

Potential energy at displacement y = E₂ (Given)

Thus,

E₁  = 1/2kx²

= x = √2 E₁/k

E₂ = 1/2ky²

= y = √2E₂/k

and E = 1/2k(x+y)² = x+y = √2E/k

= √2E₁ /k = √2E₂/k = √2E/k

= √E₁ +√E₂ = √E

Thus, the potential energy E at displacement (x + y) is = √E = √E₁ +√E₂