pulsating water pump

[filippr]

Hi everyone, my father has installed a new water pump 2 years ago, not sure about the make or model or any specifications. it seemed to be fine for over a year and a half and then recently it started pulsating when using, for example in the morning I am always the first one to wake up I try to turn on the pump either in the shower or the sink, I try to use hot water but when I open the tap fully, no water is flowing, it feels like the pump needs to be working for a while in order for it to turn on fast, I sometimes have to wait 2/3 minutes for the pump to activate, but when it does after about 4/5 minutes of use, as if it needed to warm up it works fine, I can turn it on and off as often as id like, its when it hasnt been used in awhile that it takes a few minutes to start up, then pulsates for the first few minutes and the works perfectly fine after that, the hot and cold water is connected to the pump but the cold water goes directly from the water reserve and the pump is not activated with cold water.