amp and unwanted speaker vibration

I like to seek opinion and advice from  Audiogon members.  When I connect my tube  amp (Lectron HJ50) to  my speakers ( Focus Audio Model  78) , unwanted vibration of speaker cone would occur.even  with all other equipment off.  The simultaneous vibrations from both speakers  would start to occur very rapidly and  consecutively   after I turn on  the amp for about 30 min.  However, when I plug the  amp power cord to a Belkin home theater surge protector 8 outlet extension cord (from Radio Shack), the vibration would start to occur in about 60 min, with initially only about 4 slow consecutive vibrations, then 5-9 slow vibration every 5-10 minutes.  This has been observed repeatedly.  So I think there is something wrong with my amp (it is more than 20 year old), although its performance is otherwise fine.   As the vibration  is delayed and reduced significantly by using the surge protector extension cord to supply the electricity to the amp,  I wonder if my electricity source is a problem. Would more expensive (presumable better) AC power cords on sale at Audiogon  solve the problem.?  
Your amp needs servicing. Capacitors need replacing.

"Would more expensive (presumable better) AC power cords on sale at Audiogon  solve the problem.?  "

No. The problem is with the amp. Although, if you have another pair of speakers it wouldn't hurt to try them just to be sure.

Are you saying the speakers sound/look fine for the first 30/60 minutes after turning on the amp and then the woofers start moving in/out rapidly?
Get this amp fixed before it takes out your speakers.Good luck enjoy!!
Thanks for the advices from Shadorne and mgreen27. Any thoughts as to why using Radio Shack surge protector to connect amp power cord reduces the problem significantly? If I listen to music only for one hour, then no problem is detected. 
What would be an estimated cost to replace capacitors of the Lectron tube amp?
In reference to kalali, the answer is yes. When I have turntable and preamp on and play music, no woofer vibration initially until about 60min. 

Overhaul such as replacement of caps should be in $200...250 range. Large filter caps can be expensive depending which ones you want to choose.

Thanks czarivy. A follow up question to seek advice from Audiogon members: since my Lectron HJ50 tube amp is over 25 years old, assuming it has been used 5 h a week for all these years, what other problems would I expect with continue use if I repair what is needed now? Would you advice me to buy another equivalent/ or better and newer amp? If so what would be a suitable commendation for my system (focus audio model 78 speaker,Transcendent 

Preamp, Transcendent phono preamp, Linn Sondek LP12). Thanks
That is by reputation a very good amp you own, to some a classic. I suggest keeping it taking it to a tech getting it looked over and as others have said recapped. You may find its like getting a whole new amp in terms of improved sound quality. To me that makes much more sense than ditching a very good older amp for a new one. Good luck!
I'm a firm believer in fixing well built quality gear if happy with it. I have done this several times. Most recently with a Melos 222 preamp, and currently going through the same process with a single ended amp that I've owned for a number of years. The beauty of it is that you can upgrade capacitor, resistors, wire, switches, potentiometers, etc. (in the process), to bring it to a new level of performance. It can cost a fair amount of money, but usually much less than replacing with like equipment. No regrets.   
Thanks jobs and voxer12 for sharing. I am still puzzled as to why electrical outlet with Belkin surge protector with power  filtration reduce the speaker vibration so much. 

25 years old working 5 hours per week isn't too long and not too bad overall for longevity of the unit.
if you liked unit, it would be more financially wiser to overhaul it than shopping for the new or newer model unit. 
Thanks for sharing opinions to fix my amp. 
I did one more experiment. I switched the speaker leads to 4 ohm terminal connection on my amp.( previous early onst of vibration is with 8 ohm connection)  now The vibration did not occur until about 2 h later and was just initially 4 vibrations, followed by consecutive vibrations at 2h 40 minutes. 
Does this mean circuit board of 8 ohm is not as good as 4 ohm? Any opinion from amp experts?