In a Linear, Time-Invariant (LTI) system, the frequency will not change. An excitation at 2 Hz will lead to effects at 2 Hz throughout the system. Circuits consisting only of linear, time-invariant elements (DC sources, sine sources, linear controlled sources, resistors, capacitors, and inductors) are themselves LTI systems. Your circuit consists only of these components, so it will indeed only have 2 Hz voltages and currents in its branches.1
These systems also have properties of linearity, and hence superposition. In a more complicated example, you could have an LTI circuit excitations at DC, 2 Hz, and 3 Hz, and they would lead to effects at DC, 2 Hz, and 3 Hz throughout the circuit. Each of these will occur additively, meaning that you can calculate the effect of each excitation independently and add the effects together to estimate the final response.
In contrast, there are non-linear systems where other frequencies are created. For instance, a transistor amplifier will amplify 2 Hz to 2 Hz, but it will add weak signals at 4 Hz, 6 Hz, etc., to the output as a result of the amplifier's nonlinearity. An example of this being done intentionally is mixer circuits, that intentionally convert between high frequencies (radio signals) and low frequencies (baseband) as part of communication systems.
1 In practice, some components (esp. ceramic capacitors and some inductors) can be slightly non-linear, but this effect will be very slight and might not be strong enough to create detectable signals at other frequencies. However, other inductors are intentionally made nonlinear (e.g. by saturating easily), and will produce fairly detectable harmonics. A historical example is the magnetic amplifier.