In the Tibetan Buddhist tradition, the damaru is part of a collection of sacred implements and musical instrument was adopted from the tantric practices of ancient India. These reached the Himalayas from the 8th to 12th century, persisting in Tibet as the practice of Vajrayana flourished there, even as it vanished in the subcontinent of India

The Chod damaru (or choda) is a specialized form of damaru. It is generally larger in circumference and has a more round shape than its smaller counterpart. The Chod damaru is used in the tantric practice of Chod.
Drum Damaru - The Asia and Pacific Museum in Warsaw
With no known antecedent, the chod is traditionally made of acacia wood (seng deng), though a variety of woods are acceptable, as long as the tree is not toxic and does not possess thorns or other negative attributes. Made as a one-piece, double-sided (two-headed) bell shape, size varies from 8 inches to 12 inches in diameter. Usually featuring only a thin veneer of varnish, so that the grain of the wood shows, they come the common red (marpo), black (nakpo) or rare yellow (serpo) type of acacia, and are very occasionally painted with skulls, the eight charnel grounds, or other symbols. The waist or belt is traditionally made of leather, though often brocades are used. A set of mantras are traditionally painted on the interior of the drum prior to its skinning.

The pitch of the drum varies, and the tone may vary depending on conditions of dampness, temperature and so on. Played slowly, and methodically, the droning of the damaru accompanies the haunting melodies and chants of the chod ritual, as of which are accompaniments for the inner meditations and visualizations that are at the heart of this spiritual practice.

The above applies to the ideal manufacture of the damaru, and as still described in the definitive modern work, the "Mindroling Handbook of Vajrayana Implements." Those manufactured in India and Nepal are made of indeterminate and cheap woods, with painted skins, often no interior mantras, and altogether deviating from the many other essentials, as presrcibed in technical literature such as the Mindroling Handbook. Such copies are now widespread and in use by Eastern monastics and Western students.

Chopen
Damaru of all kinds are traditionally paired with a long sash or tail called a chopen. The chopen is attached to the end of the drum's handle so that it waves about while the drum is being played. They are most commonly made of brocade or silk using the colors of the tantric elements. On smaller damaru, the chopen is usually found without adornment, but on chod damaru, the tail will often feature several items which have been sewn onto the fabric. These adornments commonly include but are not limited to: a polished silver mirror or melong, a set of small bells, strips of tiger and/or leopard skin, one or more precious stones (i.e. dzi bead), and any number of small brass trinkets.

How to Play Damaru