The displacement of two identical particles executing S.H.M are represented  by equation x1=4sin(10t+π/6) and x2=5cos(wt). For what value of 'w' energy of both the particles is same.

total energy of simple harmonic oscillator  E=12mA2ω2 m is mass; A is amplitude; ω is angular velocity given     E1=E2 12mA1 2ω12=12mA2 2ω22 ⇒A1ω1=A2ω2    ;  by question A1=4;  w1=10; A2=5 ; substitute them ⇒  4x10=5 ω22 ⇒ω2=8 units.