The 10kg block A is released from rest and slides down the s

The 10-kg block A is released from rest and slides down the smooth plane. Determine the compression x of the spring when the block momentarily stops.

Solution

-w (10 + x) sin 30 + 1/2 k x² = 0

(-10 * 9.8 * 10 sin 30) - (98.1 * sin 30 * x) + (0.5 * 5 * 10³ * x² ) = 0

(2.5 * 10³) x² - 49.1 x - 491 = 0

solving the quadratic equation

x = 0.453 m = 453 mm