If we wish to represent the equation for the position of the mass in terms of a differential equation, which one of these would be the most suitable?

m \frac{d^{2} x}{d t^{2}} + b \frac{d x}{d t} + k x = 0

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m \frac{d^{2} x}{d t^{2}} - b \frac{d x}{d t} + k x = 0

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m \frac{d^{2} x}{d t^{2}} + b \frac{d x}{d t} - k x = 0

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m \frac{d^{2} x}{d t^{2}} - b \frac{d x}{d t} - k x = 0

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Solution

The correct option is A $m \frac{d^{2} x}{d t^{2}} + b \frac{d x}{d t} + k x = 0$
The force on body oscillating in resistive medium is
$f = - k x - b v$
$\Rightarrow m \frac{d^{2} x}{d t^{2}} = - k x - b \frac{d x}{d t} \Rightarrow m \frac{d^{2} x}{d t^{2}} + b \frac{d x}{d t} + k x = 0$
k = oscillating constant
x = displacement of body from mean position
b = constant depends on resistive medium
v = velocity of object = $\frac{d x}{d t}$
m = mass of object .

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