A mass of is hung from a vertical spring of force constant

MATHEMATICS · Multi-part · IB Diploma Programme · Mathematics: Applications and Interpretation · Calculus · Calculus

Problem

A mass of

1.5\,\text{kg}

is hung from a vertical spring of force constant

60\,\text{N\,m}^{-1}

. The system experiences a resistive force

-6\dot x

and is subjected to an external vertical force

5\cos(4t)\,\text{N}

. (i) Write the differential equation governing the displacement

x(t)

measured from equilibrium. (ii) How does this equation change if the medium offers no resistive force?