Answer:
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
.