Part 1 SAQ 2 (ENGR5001)

Part 1 SAQ 2Exercise sheetCurrent spec2:115 min

ENGR5001 Part 1 Self-Assessment Questions, Q2

For a person sitting on the suspension seat below, develop a linear time invariant mathematical model showing the relationship between the floor movement $y$ and the seat position $x$ . (The seat and person are modelled as a mass $m$ supported on the floor by a spring $k$ and damper $c$ in parallel; $x$ and $y$ are vertical displacements.)

What assumptions have you made? Put the equation obtained into the standard form, indicating the steady state gain, damping ratio, natural frequency, forcing function and/or time constant.

Person on a suspension seat, modelled as mass m on spring k and damper c, floor displacement y, seat displacement x.

Formulas you may need

Newton's second law $\sum F = m\ddot x$ ; spring force $k \times$ (extension); viscous damper force $c \times$ (relative velocity) (learn this)
Generalised second order form $\dfrac{d^2x}{dt^2} + 2\zeta\omega_n\dfrac{dx}{dt} + \omega_n^2 x = Ku(t)$ (learn this)
Mass-spring-damper: $\omega_n = \sqrt{k/m}$ , $\zeta = \dfrac{c}{2\sqrt{km}}$ (learn this)