Question

Write down the DE of motion of a particle moving under the influence of gravity and experiencing a resistive force. .

Answer 1

The DE will be
`(d^2x)/(dt^2)-(k)/(m)(dx)/(dt)-g=0`

Step-by-step explanation:

We have to find differential equation under the influence of gravity and experiencing a resistive force

Let an object of mass m falling under the influence of gravity

So the force experience under gravity
`=mg`

Le the a resistive force of magnitude kv opposes this gravity force, here k is constant and v is velocity.

So net force
`F_(NET)=mg-kv`-----eqn 1

`F_(NET)=ma`

So
`ma=mg-kv`

We know that velocity is rate of change of position so
`v=(dx)/(dt)`, and acceleration is rate of change of velocity so
`a=(d^2x)/(dt^2)`

Putting all these value in eqn 1

`m(d^2x)/(dt^2)=mg-k(dx)/(dt)`

`(d^2x)/(dt^2)-(k)/(m)(dx)/(dt)-g=0`