  We simulate transverse oscillations in radiatively cooling coronal loops and
forward-model their spectroscopic and imaging signatures, paying attention to
the influence of background emission. The transverse oscillations are driven at
one footpoint by a periodic velocity driver. A standing kink wave is
subsequently formed and the loop cross-section is deformed due to the
Kelvin-Helmholtz instability, resulting in energy dissipation and heating at
small scales. Besides the transverse motions, a long-period longitudinal flow
is also generated due to the ponderomotive force induced slow wave. We then
transform the simulated straight loop to a semi-torus loop and forward-model
their spectrometer and imaging emissions, mimicking observations of Hinode/EIS
and SDO/AIA. We find that the oscillation amplitudes of the intensity are
different at different slit positions, but are roughly the same in different
spectral lines or channels. X-t diagrams of both the Doppler velocity and the
Doppler width show periodic signals. We also find that the background emission
dramatically decreases the Doppler velocity, making the estimated kinetic
energy two orders of magnitude smaller than the real value. Our results show
that background subtraction can help recover the real oscillation velocity.
These results are helpful for further understanding transverse oscillations in
coronal loops and their observational signatures. However, they cast doubt on
the spectroscopically estimated energy content of transverse waves using the
Doppler velocity.
