First slide

Applications of SHM

Question

A mass M is suspended by two springs of force constants K₁ and K₂ respectively as shown in the diagram. The total elongation (stretch) of the two springs is

Moderate

A

$\frac{Mg}{K_{1} + K_{2}}$
B

$\frac{Mg (K_{1} + K_{2})}{K_{1} K_{2}}$
C

$\frac{Mg K_{1} K_{2}}{K_{1} + K_{2}}$
D

$\frac{K_{1} + K_{2}}{K_{1} K_{2} Mg}$

Solution

For series combination $k_{eq} = \frac{k_{1} k_{2}}{k_{1} + k_{2}}$
$F = k_{eq} x \Rightarrow mg = (\frac{k_{1} k_{2}}{k_{1} + k_{2}}) x \Rightarrow x = \frac{mg (k_{1} + k_{2})}{k_{1} k_{2}}$

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