This paper describes in detail a freely vibrating reed apparatus which we have developed to study these low temperature dynamic mechanical properties of polymers (at approximately 5 cps). The apparatus is capable of measuring these properties from 4 up to 340 K. This method has the advantage over other methods of being relatively easy to set up and may be modified so more than one specimen can be investigated in a given temperature run. In addition measurements on the logarithmic decrement and Young's modulus of polystyrene are presented and compared with previous data.