A 2 kg block is suspended from the ceiling of an elevator using a...

Given $m_1 = 2 \text{ kg}$, $k = 100 \text{ N/m}$, elevator upward acceleration $a = 2.0 \text{ m/s}^2$, and taking $g = 10 \text{ m/s}^2$.

Inside the accelerating elevator, the effective acceleration due to gravity is $g_{\text{eff}} = g + a = 10 + 2.0 = 12 \text{ m/s}^2$.

At equilibrium, the restoring force balances the apparent weight of the block.

$k x_1 = m_1 g_{\text{eff}}$

$100 x_1 = 2 \times 12$

$x_1 = 0.24 \text{ m}$

When an additional mass $m_2 = 1 \text{ kg}$ is attached, the additional restoring force balances the additional apparent weight.

$k x_2 = m_2 g_{\text{eff}}$

$100 x_2 = 1 \times 12$

$x_2 = 0.12 \text{ m}$

The initial elongation is $0.24 \text{ m}$ and the further elongation is $0.12 \text{ m}$.