How to disable ringtone on iPhone 5?

I want to be able to flip the switch to be either silent or vibrate with no ringtone. I almost never use the ringtone but I often need it to be either silent (like in the library where I study 5+ hours a day) or vibrate (in my pocket most other times of day).

Note: I do NOT want to set it to vibrate on silent (and thus having the switch choose between vibrate and ringtone). I want to get rid of the ringtone completely and just switch between silent and vibrate.

Right now I only see the options:
"Vibrate on Ring" (which I want on but without the ringtone, for normal use)
"Vibrate on Silent" (which I need off because it can't vibrate in the library)

Any ideas?

You can't change the function of the mute switch, however there's a workaround.

Find/make/acquire a silent ringtone for your iPhone. Most likely, searching for "silent iPhone ringtone" with your favorite search engine will lead you to some ringtone files.

Use iTunes to sync this ringtone to your iPhone, then go into Settings > Sounds on your phone and select the newly-added silent ringtone as the default.

Note that text alerts, push notifications, etc. Will sound normally.

The other option is to try the "Do Not Disturb" function.

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