Hi

I have a basic doubt regarding the derivation of the equation of a spring mass damper system.

Suppose a mass m is connected to a spring mass damper system

O is the equlibrium position of the body which is connected to a spring and damper on the left

L ------ O ----- R

x is positive towards R.

If the body is pulled by from O and released it oscillates. At the instant it is(between O and R) x away from O and moving towards R, the FBD gives

spring force = -kx towards L

damper force = -c v where v = dx/dt

inertia force = - m a

Using DAlembert's principle we get -kx -cv - ma = 0

Thereforema + cv + kx = 0--- (1)

----------------------------

NOW the doubt :

Suppose the FBD is drawn at the instant it is(between O and R)x away from O and movingTOWARDS L

spring force = -kx towards L

damper force = c v where v = - dx/dt

inertia force = m a

Using DAlembert's principle we get -kx + cv + ma = 0

Thereforema + cv - kx = 0--- (2)

But equation (2) is not equal to eqn (1)

I am unable to find out what is wrong here.

PLEASE HELP

TIA