We can provide free sample to the customer but the shipping cost will be in custmoer side. Many customer do not want to pay the shipping cost,so we do not know how to do.
I understand your logic, but maybe it isn't correct. Maybe it is, but have you ever tried to pay for the small shipping cost to see if that would spark some sales/interest. I'd be happy to pay a postage stamp if 50% resulted in an order. I don't know what that percentage would be.
One scenario to consider is Zappos.com. They provide free shipping on all orders and free shipping on return on items. They sell shoes, and even in this scenario the "math" works for them.
Have you tried providing free samples with the shipping to them included?