Converting Dates between TimeZone

Question

I need to convert the date&time into German date&time. Problem is Calender's time zone setting seems not to work as expected or I'm implementing it incorrectly. Here is the scenario:
I/P Date String: 20100101101515 (yyyyMMddhhmmss format)
Base on condition, I need to apply offset:
I/P GMT time: During winter months apply +1 hour offset, during summer months apply +2 hour offset.
I/P London time: Apply +1 hour offset
My understanding was that the setting time zone in calender would automatically take care of winter/summer timings. But this doesn't seem to work. If anyone could provide a sample code.

Answer 1

This doesn't seem to work. Here is what I have written:
public class TimeZoneTest {
     public static void main(String[] args) throws Exception {
          String source = "20100223101500";
          DateFormat dateFormat = new SimpleDateFormat("yyyyMMddhhmmss");
          dateFormat.setTimeZone(TimeZone.getTimeZone("GMT"));
          Date date = dateFormat.parse(source);
          System.out.println("Date 1 : " + date);
          DateFormat dateFormat2 = new SimpleDateFormat("yyyyMMddhhmmss");
          dateFormat2.setTimeZone(TimeZone.getTimeZone("Europe/Berlin"));
          Date date2 = dateFormat2.parse(dateFormat2.format(date));
          System.out.println("Date 2 : " + date2);
}O/P is
Date 1 : Tue Feb 23 10:15:00 GMT 2010
Date 2 : Tue Feb 23 10:15:00 GMT 2010