A spring with a mass block at the end of it and with a stiffness of 8N/m and a relaxed length of 20cm is attached to a chamber wall that results in its oscillations being horizontal. At a particular time the location of the block mass is $\langle .38,0,0 \rangle$ relative to an origin point where the spring is attached to the chamber wall. What is the force exerted by the spring on the mass at this instant?

• Spring has relaxed length of (0.2m) $L_0=0.2m$
• Spring has spring constant of $8 N/m$
• At the moment of interest the mass block is at position $\vec{L} = \langle .38,0,0 \rangle m$
• Only force acting on system is spring force

• Origin is at chamber wall $\langle 0,0,0 \rangle$
• Assume no forces due to drag or to friction

$ {\vec F_{spring}} = -k_ss\hat{L}$

$ s = |\vec L| - L_0$

$\vec{L} = \langle 0.38,0,0 \rangle m - \langle 0,0,0 \rangle m = \langle 0.38,0,0 \rangle m$

$|\vec{L}| = 0.38m$

$\hat{L} = \dfrac{(0.38,0,0)}{0.38} = \langle 1,0,0 \rangle m$

$ s = 0.38m - 0.20m = 0.18m

$\vec{F} = -(8N/m)(0.18m)(1,0,0) = \langle 1.44,0,0 \rangle N/m$