It should be simple and cheap to build, assuming you have the basic
skills.
You would trigger a 555 monostable with a -ve going input pulse. An
improvised microswitch under the mat could be used, with appropriate
connection to the DC supply to ensure correct polarity. Or, more
expensive, a mat with inbuilt sensor, as used in commercial burglar
alarm kits. The mono's output would drive an appropriate relay
directly, assuming standard 555 with 200mA capability (100mA for the
CMOS version). Mains to the strobe light and cassette player would be
switched by the relay.
If your trigger was a +ve going pulse, then you might use a circuit
such as
http://www.terrypin.dial.pipex.com/Images/555MonoEdge.gif
You would of course need to change the RC values. In your case, for C
you could use say a 68 uF electrolytic, and for R you could
substitute a series combination of a fixed 220k with a 1M pot, to
easily accommodate the range you specified. Or use any other Rs and Cs
at hand, keeping the RC product constant.
Alternatively (one of many) you could use the neat idea already
suggested of a PIR, but add the 555 circuit to give you the variable
timing. One approach would be to arrange for the mat to switch DC
power to the alarm circuit, simultaneously triggering the alarm. A
circuit using that approach is suggested at
http://www.terrypin.dial.pipex.com/Images/555MonoByPU.gif
Have you decided what you want to do about repetitive triggering?
Please post back if the above is pitched at the wrong level.