I was a flying instructor on PA-38 Tomahawks when it was a new type in the UK. I used it exactly as I had the C150 including spinning - lots of spinning.
One turn spins above 3500' to recover above 3000' posed no problems but I became concerned about a curious vibration and "thumping" noise similar to oil canning. With a trusted student I took one up to 6000' and ordered a multi-turn spin and then turned round to observe the tail through the rear window........
I never spun that type ever again
