9. Resonance in an electrical circuit is modelled by the differential equation
$$\frac { \mathrm { d } ^ { 2 } V } { \mathrm {~d} t ^ { 2 } } + 64 V = \cos 8 t$$
where \(V\) represents the voltage in the circuit and \(t\) represents time.
- Find the value of \(\lambda\) for which \(\lambda\) tsin8t is a particular integral of the differential equation.
- Find the general solution of the differential equation.
Given that \(V = 0\) and \(\frac { \mathrm { d } V } { \mathrm {~d} t } = 0\) when \(t = 0\),
- find the particular solution of the equation.
- Describe the behaviour of \(V\) as \(t\) becomes large, according to this model.