Well, seeing from specs:
OS: Windows 7, it's old but can still run osu! fine. Not much of an issue.
CPU: E1-2500, 2 cores, 1.4 GHz. This CPU is veeeery weak, performance will be low and often unstable. You wouldn't be able to open other program along with osu! without having frequent freezes or frame drops. Stuff like streaming and screen recording are a no-no.
RAM: 4 GB, well, that's enough for osu! at least.
GPU: AMD Radeon HD 8240. Supports osu!, but still, it is a very weak GPU, it will struggle in maps with lots of notes and with non-lightweight skins...
Well, you technically can play osu! but it won't run very well.
I don't have that PC, but is similar to what your PC would do in osu! performance-wise.
A modern desktop with a low-end CPU and integrated graphics would run way better, with the plus that you can upgrade it.