Hello,
Thank you for reaching out! As far as I can find in Cisco manuals:
Cisco Catalyst 2960-X series switches support both IEEE 802.3af Power over Ethernet (PoE) and IEEE 802.3at PoE+.
That means that Your switch can only output active PoE, while TSW110 requires passive PoE to operate, meaning they are incompatible.
If powering the device via an Ethernet cable is required, there are active to passive PoE converters available for purchase online.
Why will it not work?
Active PoE works by negotiating the voltage and current needed for the end device and only then supplying it. TSW110 does not support this negotiation process and requires passive PoE, which requires the power to be delivered as soon as the cable is plugged into the LAN1 port on the device.
Quoted Cisco manual can be found here.
So just to sum up, active PoE should not be used to power TSW110, as the standards are incompatible.
Let me know if there is anything else I can help with!
Best regards,
DaumantasG