Question

A vertical spring oscillates with period 2 s with mass ‘m’ is suspended from it. When the mass ‘m’ is at rest, the spring is stretched through a distance of ______.

(Take g = π² = 10)

Options

• 4 m

• 3 m

• 2 m

• 1 m

Answer 1

A vertical spring oscillates with period 2 s with mass ‘m’ is suspended from it. When the mass ‘m’ is at rest, the spring is stretched through a distance of 1 m.

Explanation:

Given: Time (t) = 2s

g = π² = 10

For a spring-mass system:

T = `2 pi sqrt (m/k)`

⇒ 2 = `2 pi sqrt (m/k)`

⇒ `sqrt (m/k) = 1/pi`

⇒ `m/k = 1/pi^2`

Extension at equillibrium (x) = `(m g)/k`

= `g * m/k`

= `g/pi^2`

= `10/10`

= 1 m