Question

A vertical spring oscillates with period of 6 s with mass 'm' suspended from it. When the mass is at rest, the spring is stretched through a distance of ______.

(Take g = π²)

Options

• 5 cm

• 7 cm

• 9 cm

• 3 cm

Answer 1

A vertical spring oscillates with period of 6 s with mass 'm' suspended from it. When the mass is at rest, the spring is stretched through a distance of 9 cm.

Explanation:

`T = 2pisqrt(m/k)`

mg = kx ⇒ x = `(mg)/k`

`x = g(T/(2pi))^2`

Given:

T = 6 s

g = π²

Then: `x = pi^2 · (6/(2pi))^2 = pi^2 · (3/pi)^2 = pi^2 · 9/(pi^2) = 9` cm