Jason Hsu wrote:
It's part of a design for a T/R sense circuit for a noise cancellation
device.

I won't bore you with too many details. One thing I noticed in a
design I'm looking at is that 1W resistors could be subject to as much
as 50W of power apiece during the time it takes for a relay to
respond. This response time is 7msec. The overall duty cycle will be
low (well under 1%).

Can the 1W-51 ohm resistors handle this 50 RF volts 0-peak (about 50W
PEP) for .007 sec? 50W over .007 seconds is .35 Joules. .35W for 1
second is also .35 Joules, which a 1W resistor should have no trouble
handling. Can the resistors be damaged during that .007 seconds?

Your question is improper- no mention of resistor type - almost any
resistor type can take the limited overload if you up the steady state
power rating. When in doubt go with bulk ceramic- these products are
well characterized for pulsed overload operation and used in RF apps.
http://www.globar.com/ec/resistor.php.html


Also, how much time does it take to damage a toroid? If it can handle
X units of flux density continuously, how much flux density can it
handle for .007 seconds with a low overall duty cycle (like well under
1%)?

This will be easier because the heating time constant is longer and RF
is reflected away when it saturates- you will have to measure this
yourself- it is unlikely any manufacturer has done it.