That should be working fine try another headset just to make sure where the problem lies. Once you try another headset you will know whether the problem is with your headset or your phone jack.
<br> When you insert your headphone and play music, I presume your built-in speaker does not operate. If so, the headphone jack is clearly being recognized (triggering the physical cut off) but the signal is not getting to your headphones.
<br> Sometimes crud (technical term) can get inside the jack opening preventing proper connections. Try and use compressed air to clear it out. That doesn't work, you can feel around with sharp needle but be very careful when you do that.
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<br> Best of luck