That could be tricky... These "household" AC-powered LED lights have a power supply built-in and the turn-on & turn-off are undefined. I'd recommend you try it with a regular light switch to see if you can "pulse" it on & off cleanly the way you want.
If the manual switch works for you, you can use a relay with the Arduino to do the same thing under software control. (A relay is an electrically-controlled, electrically-isolated switch.) You can't drive an regular (electromechanical) AC relay directly with the Arduinobut you can find relay boards with a built-in driver circuit. You can easily find solid-state relays that can be driven directly from the Arduino. Solid state relays are easier to use and they often have screw-connectors so they are easy to wire-up, but they are more expensive.
Any Arduino will do.
...pulsate using Arduino.
...I'd like it to look as smooth as possible.
What do you mean by "smooth". A "pulse" is instantly on & off.
Do I have to buy a dimmer?
That lamp is not dimmable. If it's dimmable it will say so. Also, notice that it says "AC85-265V". That means it's internal power supply will maintain constant brightness as the AC voltage varies.
[u]AC light dimming[/u] is more complicated than PWM-dimming a regular little LED. (And of course, the AC zero-crossing detector and the AC output must be electrically isolated from the 5V Arduino.)
P.S.
If you are an artist and not an electronics hobbyist and you don't want to get into the nitty-gritty electronics, look into [u]DMX512[/u] ((theatrical & DJ lighting).
Of course, you can build a DMX controller (or DMX-controlled lights) with the Arduino, but the idea would be to buy a stand-alone controller or a DMX computer interface.
Thought I saw that bulb said dimmable, might've been looking at a related product.
So, unless it says dimmable, it's safer to assume it won't work. Some bulbs specify dimmable or non-dimmable, it's a gamble for those that don't specify because some actually are.
So, unless it says dimmable, it's safer to assume it won't work. Some bulbs specify dimmable or non-dimmable, it's a gamble for those that don't specify because some actually are.
It would be a risky gamble if it doesn't say dimmable. Building a dimmable power supply into an LED bulb is more complicated than building-in a non-dimmable power supply so a dimmable LED bulb usually costs more.
A regular-old incandescent bulb is just a filament in a vacuum and they are all dimmable. (Most fluorescent bulbs are not dimmable.)
And if you need dimming, forget what I said about relays.... Relays are on/off.