Yes, particles in a solid vibrate when at room temperature. In fact, all particles, regardless of their state (solid, liquid, or gas), are constantly in motion. The amount of motion depends on the temperature of the substance. At higher temperatures, particles move more quickly, while at lower temperatures they move more slowly.

The particles in a solid are held in place by strong intermolecular forces, which prevents them from moving very far. However, they can still vibrate in place. The vibrations of the particles in a solid are what cause the solid to feel warm to the touch.

The amount of vibration that occurs in a solid depends on the temperature of the solid and the type of material. Some materials vibrate more than others at the same temperature. For example, metals vibrate more than non-metals. This is why metals feel colder to the touch than non-metals, even when they are at the same temperature.