The mass m in Fig. 1 is connected to a spring-damper support through a rigid pulley...

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The mass m in Fig. 1 is connected to a spring-damper support through a rigid pulley of radius r and polar moment of inertia J about an axis perpendicular to the disk's centre O. Assume that the contact between the disk and the transmission string is no-slip, and that the string is inextensible. M(t) x J m 150 (41 K Fig. 1: Mass connected to a spring-damper through a pulley. Refer to the system in Fig. 1. The damping ratio is determined to be Ç= 0.03, and M(t) is a torque parallel to the disk's axis of rotation, acting on the disk. The other parameters are the same as above. 1. (10pt) Obtain the governing equation of the system with damping and external torque included. The mass m in Fig. 1 is connected to a spring-damper support through a rigid pulley of radius r and polar moment of inertia J about an axis perpendicular to the disk's centre O. Assume that the contact between the disk and the transmission string is no-slip, and that the string is inextensible. M(t) x J m 150 (41 K Fig. 1: Mass connected to a spring-damper through a pulley. Refer to the system in Fig. 1. The damping ratio is determined to be Ç= 0.03, and M(t) is a torque parallel to the disk's axis of rotation, acting on the disk. The other parameters are the same as above. 1. (10pt) Obtain the governing equation of the system with damping and external torque included.

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Solution We have dx dt 2 becomes dt x dx 2x 88 x 8x 2x 8 36x Integrating ... View the full answer