Answer
$v_2=16.4~m/s$
Work Step by Step
We can determine the required speed as follows:
According to the conservation of energy equation
$T_1+V_1=T_2+V_2$
$\implies 0+\frac{1}{2}kx_1^2=\frac{1}{2}mv_2^2+\frac{1}{2}kx_2^2$
We plug in the known values to obtain:
$\frac{1}{2}(50)(3.7)^2=\frac{1}{2}(2)v_2^2+\frac{1}{2}(50)(1.7)^2$
This simplifies to:
$v_2=16.4~m/s$
