Final video is faster than what I see in the viewport I have a walk cycle that plays at correct speed in the 3D viewport. But after making a final video the video plays too fast. This fast speed happens whether I use FFmpeg or AVI jpeg. Nothing changes when I alter the fps from 29.97 to 60.

I should say that my timeline is set to 'no sync' which is what it's always been set to. However, when I change the timeline setting to 'frame dropping' or 'AV sync' I can see the speed in the 3D viewport plays at the same speed as the final rendered videos (which is way too fast).

I've had this problem for a week and can't find the answer. Any help would be greatly appreciated.
I would never trust playback in blender to be a representation of anything resembling real-time. It really depends on how powerful your computer is. For the most part, preview in the 3d viewport it is usually slower unless you are visualizing on a very simplified mode, like Bunding Box, maybe wireframe and with low settings on modifiers or anything that can help your computer cope with the demands of the scene. If the speed looks fast when you play using frame dropping i probably means that the animation might indeed need to be slowed down. When using Frame Dropping the computer is trying to target the desired frame rate by not generating all of the frames in the animation. To do tests renders use OpenGL rendering (as suggested by @moonboots) It will give you a better sense of what your animation looks like in real-time.

You can of course change the final output's speed by altering the Time-Remapping See: How can I modify the frame rate without changing the overall animation speed?