first pull the spark plug boot off and check for tracks, then check the spark plug condition , it's gonna be 1 of 3 things the spark plug itself , injector , or spark plug boot. it could also be the plug wire.
most likely misfiring cylinder(s) and/or worn engine mounts.
Is it a 4 cylinder? Sometimes a 4 cylinder engine will shake a little extra when the AC is running and it's at an idle. You might be able to step up the idle a little extra but 4 cylinder engines are notorious for shaking when the AC is running.
Try having your front suspension aligned. Check your ignition system for misfiring as well.
The answer is on page 11 in the owner's manual ( "Light is blinking" ). Engine is misfiring, bring it to a garage as soon as possible.
A cylinder misfiring can cause this sympton, check/replace spark plugs and plug wires. Also, sputtering and shaking can be caused by engine timing, have the timing checked. Another cause can be fouled fuel injectors on fuel injected vehicles.
One or more cylinders on one side is/are not firing. Check by pulling a plug wire while the engine is running. If there is no change when you pull the plug wire than that cylinder is not doing anything. Replace the plug wire and pull another until you find the one that, when pulled does not affect the engine.
The kink stops the mercury from falling, giving the user/reader of the thermometer time to read the highest temperature recorded. Shaking the thermometer lets the mercury fall again.
Cylinder missfire perhaps ? Get it scanned.
In general, engine "shaking" is caused by a misfire in one or more cylinders. That can be caused when a multiport injector is plugged or faulty, a plug wire or sparkplug is faulty or one or more cylinders have low compression. Try to isolate the cylinder that's not firing. Plastic pliers are available for pulling plug wires. Pull one plug wire at a time and see which one DOESN'T make a difference. When you pull the plug wire from a cylinder that's running, that cylinder will stop firing and the engine will run worse. If you come across a cylinder that was already misfiring, the engine won't run any worse by disconnecting the plug. Once you've isolated the cylinder, check the plug. If it's fouled or wet, it's possibly an ignition problem, check the wire(s) and possibly replace the plugs. On the other hand, while you have the plug out, check the compression on that cylinder, it should be above 100 PSI, or at least very near to it. If the plugs are good, and the compression is up, start being suspicious of the injector.
Could be any number of reasons. First if the check engine light is on, make sure you read the codes which will give you clues as to what is wrong. It could be a misfiring cylinder, bad/dead spark plug, warped cylinder, damaged or missing motor mount, or even a damaged/worn timing chain. A simple cause would be bad fuel or water in fuel, or a clogged air filter. Check your oil level, spark plugs, and air filter first, these are easy and inexpensive to replace.
Not running on all cylinders? Engine light on? Bring to shop to have scanned
The Corolla could be shaking for many reasons. Start by checking the wheel bearings and brakes for wear. Then check the engine to see if it running rough, causing the shake.