I initially created an hasty example in this ProShow Presenter version.
Later, just for fun, I decided to try another example, but using a horizontal pivot. Briefly, if you tried the settings in the link above, it's very similar except that instead of using vertical tilt, horizontal tilt was used. The KF settings 2-6 are still set about .15 of a second apart between the swings except that KF 1 - KF 2 are separated by .25 of a second. The keyframe timing is the same regardless of the chosen center rotation point.
If the swing timing isn't quite to your liking, experiment with the tilt key frames and settings. It might be helpful to note the setting was halved after the first back-and-forth full swing in the example to get a feel of how you might want to make further adjustments faster or slower, more swing or less swing. You may prefer removing the 2 key frames with the -15 and 15 settings and which would decrease total key frames to 5 instead of 7. It just depends on how you want the end result to look like.
Due to ever changing captions, font, font size, alignment, etc, the center rotation point setting will likely need to be different each time the effect is created and for each layer. Use the scrubber to playback the action and make adjustments until you're happy with the results. Intuitive positioning of the center rotation point seemed to get easier the more I played with it.
Here are the sample settings so you don't have to write them down during playback:
In the example:
* Pivot = left side
* Alignment = center
* Font = Times New Roman
* Font Size = 30
Slide transition in and out: 1
Slide time: 3
Insert text layer and type "Swinging Text"
Text Settings: PAN 50/50
Use CUT on Text Layer KF 1 Transition IN
Rotation Ctr X: -20 across all key frames
Time Horizontal Tilt
KF 1 - 1.05 Cut --- 90
KF 2 - 1.30 -------- -30
KF 3 - 1.45 -------- 30
KF 4 - 1.60 -------- -15
KF 5 - 1.75 -------- 15
KF 6 - 1.90 -------- 0
KF 7 - end Fade --- 0
The fun little variations of the effect that appear at the end demonstrate text flip-swinging from top, bottom, left and right. For vertical swing, populate the vertical tilt settings with the KF settings above instead and set horizontal tilt settings to "0".
Hope that makes sense.
This technique is not restricted to just text layers. Try it out on image layers too! Having the tilt feature now in ProShow version 6 makes a page turn effect much easier to achieve than it was to create the effect years ago without the tilt feature.
Since there is no category for tutorials in this community, I'm not sure I put this in the proper category. Forgive me if I picked the wrong one....
Horizontal Swinging Text - A ProShow Producer 6 Tutorial