The vertical displacement yyy metres of a heavy-duty hydraulic damper from a fixed point OOO at time ttt seconds is modelled by the equation
y=σ+12t−μe−0.5t y = \sigma + 12t - \mu e^{-0.5t} y=σ+12t−μe−0.5twhere σ\sigmaσ and μ\muμ are constants. At time t=3t = 3t=3, the acceleration of the damper is measured as −0.8 m s−2-0.8 \text{ m s}^{-2}−0.8 m s−2.
Show that μ≈14.3\mu \approx 14.3μ≈14.3.
Given that the damper has an initial displacement of 5 metres from OOO, determine the value of σ\sigmaσ. Give your answer to two significant figures.