First slide

Applications of SHM

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 mass is released with the spring initially unstretched. Then the maximum extension in the spring is

Moderate

A

4 Mg/K
B

2 Mg/K
C

Mg/K
D

Mg/2K

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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