Question

Determine an expression for the time from when the block collides with the spring to when the spring reaches maximum compression

Answer 1

1/2 m v^2 = 1/2 k x^2 energy of block will be transferred to spring

1/2 m (x/t)^2 = 1/2 k x^2 x/t max speed of block

t^2 = m / k

t = (m/k)^1/2 = 1 / ω since ω = (k / m)^1/2 for SHM

ω = 2 π f = 2 π / T where T is period

T = 2 π * (m / k)^1/2

t = T / 4 = π / 2 * (m / k)^1/2 1/4 period needed for 1/4 oscillation