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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 $(U_{gravity})$ is assume to be 0. Potential energy U will change with displacement x of the block as

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b

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c

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d

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answer is A, C, D.

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Detailed Solution

at equilibrium position mg =kx $\Rightarrow x = \frac{m g}{k}$
At maximum compression $\frac{1}{2} k x^{2} = m g x \Rightarrow x = \frac{2 m g}{k}$
$U_{spring} = \frac{1}{2} {kx}^{2}$ where x is compression.
$U_{gravity} = - mgx$
$U_{s p r i n g} + U_{g r a v i t y} = \frac{1}{2} k x^{2} - m g x,$ 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