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A block of mass m is placed on a massless spring (initially unstretched) and released. Due to mass, oscillation starts. There is no loss of energy and initially gravitational potential energy Ugravity is assume to be 0. Potential energy U will change with displacement x of the block as

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Detailed Solution

at equilibrium position mg =kx  ⇒x=mgkAt maximum compression   12kx2=mgx⇒x=2mgkUspring=12kx2 where x is compression.Ugravity=−mgx Uspring+Ugravity=12kx2−mgx, represents a parabola equation.
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A block of mass m is placed on a massless spring (initially unstretched) and released. Due to mass, oscillation starts. There is no loss of energy and initially gravitational potential energy Ugravity is assume to be 0. Potential energy U will change with displacement x of the block as