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**A small metal block of mass m is placed on a smooth horizontal table and constrained to move along a frictionless, rectilinear groove, The block is attached to one end of a spring (of spring constant k) whose other end is fastened to a pin P.**

Let length L be the equilibrium length of the spring and the perpendicular distance to the groove, The spring is now pulled a distance Xo from the equilibrium position and released. Show that, if the displacement along the groove x « t. the restoring force on

the block is proportional to x ^3 , so the motion is not simple harmonic although it will still be periodic). [Hint: For x « L, x^2 + L^2 "" L + (x^2 /2L).]

Let length L be the equilibrium length of the spring and the perpendicular distance to the groove, The spring is now pulled a distance Xo from the equilibrium position and released. Show that, if the displacement along the groove x « t. the restoring force on

the block is proportional to x ^3 , so the motion is not simple harmonic although it will still be periodic). [Hint: For x « L, x^2 + L^2 "" L + (x^2 /2L).]

**General spring and harmonic , periodic motion formulas**

**I thought the cosine of the F force on the spring is the responsible force i.e. restoring force and sine of F has no importance, therefore Fcosineø = -k x .. but from there I get nowhere :(**