A vertical spring oscillates with period 6 second with mass m is suspended from it. When the mass is at rest, the spring is stretched through a distance of (Take, acceleration due to gravity, g = π 2

Question

A vertical spring oscillates with period 6 second with mass m is suspended from it. When the mass is at rest, the spring is stretched through a distance of (Take, acceleration due to gravity, g = π 2 = 10 m / s 2 )

TestHub · Accepted Answer

The time period of a vertical spring-mass system is given by $T = 2 π \frac{m}{k}$ .

When the mass is at rest, the spring is stretched by a distance $x$ such that the restoring force balances the weight:

$k x = m g \Rightarrow \frac{m}{k} = \frac{x}{g}$

Substituting this into the time period formula:

$T = 2 π \frac{x}{g}$

Given $T = 6$ s and $g = π^{2}$ :

$6 = 2 π \frac{x}{π ^{2}}$

$6 = 2 π \frac{x}{π}$

$6 = 2 x$

$x = 3$

$x = 9$ m

Answer: 9 m

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