QUESTION $8$

A $8$ pound weight stretches a spring $4$ feet. Assume the surrounding medium offers a damping force of $4$ times the instantaneous velocity. The mass is driven by an external force of $25cost.$

The correct differential equation for the position, $x(t),$ of the mass at a function of time, $t,$ is

$($Use $g=32f\frac{t}{s^2})$

Select the correct answer

a$.\frac{1}{2}\frac{d^{2}x}{d{t}^2}+4\frac{dx}{dt}+4x=25cost$

b$.4\frac{d^{2}x}{d{t}^2}+\frac{dx}{dt}+4x=25cost$

c$.\frac{1}{4}\frac{d^{2}x}{d{t}^2}+4\frac{dx}{dt}+2x=25cost$

d$.\frac{d^{2}x}{d{t}^2}+\frac{1}{4}\frac{dx}{dt}+4x=25cost$

e$.\frac{d^{2}x}{d{t}^2}+4\frac{dx}{dt}+4x=25cost$