I went under my car today and notice the torque engine mount was broken. However I was unable to determine if the other engine mount were broken. The engine does moves when shifting gears but I don't know if its because of the broken torque mount.

The only thing I can say about this engine mounts is the cables around them were loose. I'm referring to this one.

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Does it need replacement?

 

if its broken fix it
the engine moving too much isent all that great
if it helps the cable on mine is quite tight (however i dont really know what your asking)

 

if your car is close to 100k miles, then yes replace all the engine mounts