Question

Write down the DE of this damped harmonic oscillator.

Answer 1

`(d^(2)x )/(d^(2)t )+(k)/(m)x+(b)/(m) (dx)/(dt)=0`

Step-by-step explanation:

The spring mass equation for the damped oscillation will be,

`F=-kx-bv`

Here, -bv is the damping term used in this b is damping constant, k is spring constant, x is elongation in the spring, F is the force.

`ma=-kx-bv\\m(d^(2)x )/(d^(2)t )=-kx-b(dx)/(dt)\\  m(d^(2)x )/(d^(2)t )+kx+b(dx)/(dt)=0\\(d^(2)x )/(d^(2)t )+(k)/(m)x+(b)/(m) (dx)/(dt)=0`

Therefore the differential equation for the damped harmonic oscillator is,

`(d^(2)x )/(d^(2)t )+(k)/(m)x+(b)/(m) (dx)/(dt)=0`