Maths and Vibrations: Tutorial Sheet 9 Solutions

b) Inertia

2) b) (see course book part 2)

6) Total energy of system remains constant throughout motion, therefore, consider one extreme.

7) At zero displacement total energy is kinetic, therefore velocity amplitude is given by,

At maximum displacement total energy is potential, therefore displacement amplitude is given by,

a) b)

c) d) (one spring pulls the other pushes in same direction)

Total spring stiffness is given by,

For the parallel case, resonant angular frequency is given by,

For the series case, resonant angular frequency is given by,

From the two equations, k₁ and k₂ can be found, by eliminating each in turn from the second equation one will find,

k₁ =100000 Nm^-1 and k₂ = 300000 Nm^-1.