Dancing wire

In the circuit above, wire \(AB\) has length \(40\text{ cm}\) and resistance per unit length \(\SI[per-mode=symbol]{0.5}{\ohm\per\centi\meter}\). The voltmeter is ideal.

If we want to make the reading in the voltmeter vary with time as \( V(t) = 2 \sin(\pi t) \ \si{\volt},\) then what should be the velocity of the contact (the arrow-tipped end of the wire above) as a function of time?

If the velocity can be expressed as \(A\sin(\omega t+\phi) \text{ cm}\,\text{s}^{-1}, \) where \(0<\phi<\pi \), then enter the value of \( \dfrac A{\omega- \phi} \).

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