Core Pure- SHM Modelling

acceleration , x double dot

acceleration , x double dot

= -w^2 x

acceleration, x double dot also written as

v dv/dx

Damped harmonic motion equation

Has dx/dt term

Equal to 0

Heavy damping

Auxiliary equation has distinct real roots

Critical damping

Auxiliary equation has equal roots

Light damping

Auxiliary equation has no real roots

Forced harmonic motion equation

Non-homogenous

Equal to a function of t

Coupled first-order differential equations are only homogenous if

+f(t) or +g(t) equal to 0