First slide

Simple hormonic motion

Question

An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The rnass is released with the spring initially unstretched. Then the maximum extension in the spring is

Moderate

A

$\frac{4 Mg}{K}$
B

$\frac{2 Mg}{K}$
C

$\frac{Mg}{K}$
D

$\frac{Mg}{2 K}$

Solution

Let x be the maximum extension of the spring. From energy conservation
Loss in gravitational potential energy = Gain in potential energy of spring
$Mgx = \frac{1}{2} {Kx}^{2}$
$\Rightarrow x = \frac{2 Mg}{K}$

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