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 .

total distance/total time

(85 + 82)/(5+3)

167/8

20 just over

energy stored in the capacitor= 9.72 x 10⁻⁴ j

explanation:

the energy stored in the capacitor is given by

e= 1/2 c v²

e= energy stored

c= capacitance= 1.5 µc= 1.5 x 10⁻⁶f

v= potential difference=36 v

so energy stored= e= 1/2 (1.5 x 10⁻⁶) (36)²

energy stored= 9.72 x 10⁻⁴j