Amass of 4kg stretches a spring 40cm. suppose the mass is displaced an additional 12cm in the positive (downward) direction and then released. suppose that the damping constant is 3 n⋅s/m and assume g=9.8m/s2 is the gravitational acceleration. (a) set up a differential equation that describes this system. let x t

A differential equation is .

Explanation:

Given that,

Mass = 4 kg

Stretch string = 40 cm

Additional distance = 12 cm

Damping constant = 3 N-s/m

Let xx to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x,x′,x′′ .

We need to calculate the spring constant k

The net force in y direction at equilibrium position

Put the value into the formula

The initial displacement from equilibrium

The initial velocity is

We need to set up a differential equation

The net force in y direction is zero at equilibrium position .

Put the value into the equation

Hence, A differential equation is .

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14

a, c, d, e are all applying about success strategies.