When a copper plate is placed below an oscillating magnetic needle then the magnetic needle stops soon. Since, the magnetic needle is an oscillating needle then it placed in some a magnetic field. If a good conductor(copper plate) is placed below the oscillating needle, then it stops. Because the applied charge by electric field is transferred to conductor i.e., in other means the conductor itself gets charged and produced magnetic field which opposes the deflection in needle and came it so stop.
Since glass is bad conductor of electricity and do not get magnetize therefore, it has no effect on magnetic needle when placed below the magnetic needle.