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Unfortunately, we need more information. First, you should fill in the Profile using the Profile button at the top of this web page. That way, your computer specifications will always be available in case you come back to this forum with more questions in future.
We need to know those specifications in this case. We also need to know which format you have chosen to capture in. If, for example, you have chosen to capture in DVD format (mpeg-2), then the incoming analogue signal is converted by Video Studio to mpeg-2 on the fly. The incoming data goes into what is called a 'transcode buffer' where it waits until it can be converted to mpeg-2. When that conversion happens, the buffer empties, ready for more data to be received and processed.
However, if you have only an average computer, sometimes its resources are not enough to be able to convert the analogue signal to mpeg-2 quickly enough, and the transcode buffer fills up totally. As your computer works overtime to process it, the resulting video stream coming out of your transcode buffer slows down, and in some extreme cases with under-powered computers, may even stop entirely.
That is a negative feature of simple capture devices like EasyCap as they really only provide an interface between your VCR and computer. They don't actually do any work in converting the incoming signal. Instead, they merely channel it to the computer, and the computer has to do all the work. There are more expensive (but well under $100) devices which have a hardware chip built into them which actually does the conversion to mpeg-2 within the device, and the computer then has plenty of resources to display the resulting video correctly.