Motor (4; 104) of the linear electrodynamic type, for compressing a fluid circulating in a cryogenic cooler (1; 101) in particular of the Stirling cycle type, the motor (4; 104) comprising: - at least one power supply circuit (8.1, 8.2; 108.1, 108.2) suitable for delivering, an AC power supply current (I1, 12; 1101, 1102) with an AC power supply voltage (U1, U2; U101, U102); - at least one movable mass (10.1, 10.2; 110.1, 110.2), such as a piston, following a translation movement between a first position and a second position wherein the respective movable mass (10.1, 10.2; 110.1, 110.2) can compress the fluid; and - at least one induction coil (5.1, 5.2; 105.1, 105.2) connected to the power supply circuit (8.1, 8.2; 108.1, 108.2) and arranged so as to impress the translation movement on a respective movable mass (10.1, 10.2; 110.1, 110.2); - at least one secondary circuit (14.1, 14.2; 114.1, 114.2) arranged to be connected to the terminals (15.1, 15.2; 16.1, 16.2) of at least one induction coil (5.1, 5.2; 105.1, 105.2); and - at least one switching member (21, 22; 121, 122) arranged so as to selectively connect the secondary circuit (14.1, 14.2; 114.1, 114.2) to at least one induction coil (5.1, 5.2; 105.1, 105.2); - the secondary circuit (14.1, 14.2; 114.1, 114.2) comprising at least one compensation component (R1, R2, C1, C2; R101, R102, C101, C102) suitable for producing a phase shift between said AC power supply voltage and said AC power supply current (I1, I2; 1101, 1102), so as to reduce the shift that the inductance of the induction coil (5.1, 5.2; 105.1, 105.2) produces between said AC power supply voltage (U1, U2; U101, U102) and said AC power supply current (I1, I2; 1101, 1102), the motor (4; 104), being characterised in that, the or each switching member (21, 22; 121, 122) has: - a first position, wherein the respective secondary circuit (14.1, 14.2; 114.1, 114.2) is connected to the respective induction coil (5.1, 5.2; 105.1, 105.2); and - a second position, wherein the respective secondary circuit (14.1, 14.2; 114.1, 114.2) is disconnected from the respective induction coil (5.1, 5.2; 105.1, 105.2); and wherein the or each switching member (21, 22; 121, 122) is arranged such that: - in the first position, the respective power supply circuit (8.1, 8.2; 108.1, 108.2) is disconnected from the respective induction coil (5.1, 5.2; 105.1, 105.2); and - in the second position, the respective power supply circuit (8.1, 8.2; 108.1, 108.2) is connected to the respective induction coil (5.1, 5.2; 105.1, 105.2). - at least one power supply circuit (8.1, 8.2; 108.1, 108.2) suitable for delivering, an AC power supply current (I1, 12; 1101, 1102) with an AC power supply voltage (U1, U2; U101, U102); - at least one movable mass (10.1, 10.2; 110.1, 110.2), such as a piston, following a translation movement between a first position and a second position wherein the respective movable mass (10.1, 10.2; 110.1, 110.2) can compress the fluid; and - at least one induction coil (5.1, 5.2; 105.1, 105.2) connected to the power supply circuit (8.1, 8.2; 108.1, 108.2) and arranged so as to impress the translation movement on a respective movable mass (10.1, 10.2; 110.1, 110.2); - at least one secondary circuit (14.1, 14.2; 114.1, 114.2) arranged to be connected to the terminals (15.1, 15.2; 16.1, 16.2) of at least one induction coil (5.1, 5.2; 105.1, 105.2); and - at least one switching member (21, 22; 121, 122) arranged so as to selectively connect the secondary circuit (14.1, 14.2; 114.1, 114.2) to at least one induction coil (5.1, 5.2; 105.1, 105.2); - the secondary circuit (14.1, 14.2; 114.1, 114.2) comprising at least one compensation component (R1, R2, C1, C2; R101, R102, C101, C102) suitable for producing a phase shift between said AC power supply voltage and said AC power supply current (I1, I2; 1101, 1102), so as to reduce the shift that the inductance of the induction coil (5.1, 5.2; 105.1, 105.2) produces between said AC power supply voltage (U1, U2; U101, U102) and said AC power supply current (I1, I2; 1101, 1102), - a first position, wherein the respective secondary circuit (14.1, 14.2; 114.1, 114.2) is connected to the respective induction coil (5.1, 5.2; 105.1, 105.2); and - a second position, wherein the respective secondary circuit (14.1, 14.2; 114.1, 114.2) is disconnected from the respective induction coil (5.1, 5.2; 105.1, 105.2); and - in the first position, the respective power supply circuit (8.1, 8.2; 108.1, 108.2) is disconnected from the respective induction coil (5.1, 5.2; 105.1, 105.2); and - in the second position, the respective power supply circuit (8.1, 8.2; 108.1, 108.2) is connected to the respective induction coil (5.1, 5.2; 105.1, 105.2).