Question

Derive the differential equation for damp oscillation and write down the solution of the differential equation?

Answer 1

Answer:

First go for simple harmonic oscillation.

force eqn is,

F = -Kx ........ (1)

(-ve sign due to opposite direction of Force and displacement)

now,

there will be a draging force to oppose the motion and it depends on Velocity....

Fd = -bV ...... (2)

again -ve sign due to opposite direction of Dragging force (Fd) and velocity (V) , and "b" is a constant.

So, net Force in damped Motion,. .

F = -Kx - bV ..... (3)

but we know,

so, putting these values in eqn (3)...

or,

this is the eqn for damped oscillation...

Explanation:

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