[RPG] If Heat Metal is cast on a shield, could the target be forced to drop it

RAW there really is only one option to quickly take off armor: have someone help you.

Getting Into and Out of Armor

The time it takes to don or doff armor depends on the armor’s category.

Don. This is the time it takes to put on armor. You benefit from the armor's AC only if you take the full time to don the suit o f armor.

Doff. This is the time it takes to take off armor. If you have help, reduce this time by half.

The fastest a PC could shed heavy armor with help would be in 2 and a half minutes or 25 rounds of combat.

RAW options to avoid the damage

1. Run away. As I interpret the spell you would still need to be in its range to use the bonus action attack. Running out of range would be difficult to achieve since the spell attack is a bonus action allowing the caster to use both their actions to follow you. However if allies impede the movement of the caster or your move speed is greater it could be accomplished in one round.
2. Deal Damage. Every time the magic user takes damage while concentrating on a spell they are forced to make a CON save to keep that spell up. If everyone hits the wizard odds are pretty high that he will fail one of those CON saves.

Houserule option

Let the PC take it off with a standard action, but doing so damages the armor, preventing them from wearing it again until they have it repaired.

Musings on Heat metal

There is no requirement for a PC or NPC whose gear is affected by heat metal to react taking off their armor. The stipulation of the spell is to throw it if they can, donning and doffing seems to be a bit more than all that and as such I would interpret it to mean weapons should be thrown, but armor can be kept on. I know 2d8 bonus action damage sounds like a lot, but dice only damage has a way of only coming out to be around the average most of the time, while 9 damage a round without an attack roll is pretty nice, it is probably a better idea for the party to focus-fire on the wizard to end it rather than someone in heavy armor taking their armor off and seriously lowering their AC for the rest of the fight.

There is no requirement to start doffing your armor: the clause in question on the spell is "drop the object if it can" where if is the operative word here. You can't simply "drop" armor, so you aren't required to take it off.

If you want to avoid the damage, there are a few different options here:

1. You can start doffing your armor. This takes a long time depending on what you're wearing, and if you have help it's halved, but this is a terrible option in combat.

2. Try to break the caster's concentration. The spell is concentration, so if you can do a good bit of damage, you can force them to make concentration saves. If you have a multi attack, they have to make a save every time they are hit.

3. Run away. This is GM-dependent as there is not necessarily a requirement that they stay in range to use the bonus action (though there probably is, this is up for debate). If your GM allows, running out of the range of the spell is potentially the best option here.