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 .

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explanation:

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