oscillations are not simple harmonic oscillations Solutio The mass is pulled out a distance x along the rail, the new total length of the spring is So the x-component of the force that the spring exerted on the mass is F=FcosB=-k[( +x)-lo]cos 8 From the diagram, cos so the x-component of the force +l0 F=-k(x )=-kx(1 )=-kx(1 For x<<lo=()<<l, the x-component of the force F≈-k1-1()2+1 +1=1 hen F s-k(1-11 x2 Thus when the mass is released from the point x along the rail, the oscillations occur but their oscillations are not simple harmonic oscillationsoscillations are not simple harmonic oscillations. Solution: The mass is pulled out a distance x along the rail, the new total length of the spring is 2 2 0 l = l + x So the x-component of the force that the spring exerted on the mass is cosθ [( ) 0 ]cosθ 2 1 2 2 0 F F k l x l x = = − + − From the diagram , 2 0 2 cos x l x + θ = , so the x-component of the force is ) ( ) 1 1 ( ) (1 2 0 2 0 2 0 + = − − + = − − l x kx x l l x F k x x ) ( ) 1 ( ) 1 (1 2 0 2 0 + + = − − l x l x kx For ( ) 1 2 0 << 0 ⇒ << l x x l , the x-component of the force is [1 ( ) 1] 2 0 ≈ − − + l x F kx x Since + = − 2 −L 0 2 0 ( ) 2 1 ( ) 1 1 l x l x Then 3 2 0 2 0 2 2 ) 2 1 (1 1 x l k l x F kx x ≈ − − + ⋅ = − Thus when the mass is released from the point x along the rail, the oscillations occur but their oscillations are not simple harmonic oscillations