081117-0752 EST
starcrossed:
Using a different calculation and my dimensions:
To raise 30 # to the 45 deg angle at the end of a 3 ft pivot arm is a rise of 3 - 0.707*3 ft = 0.879 ft. This is 30*0.879 ft-# of work. If this is done in 1.5 seconds, then the rate is 30*0.879/1.5 ft-#/sec = 26.37/1.5 = 17.6 ft-#/sec .
Since 1 HP is equivalent to 550 ft-#/sec we should need 17.6/550 HP = 0.032 HP or 24 W.
I did the calculations mentally and was obviously suffering from brain fade at the time.
Taking your figures, 3ft is about 1 metre, and 15kg exerts a force due to gravity of 150 Newtons (using the approximation that g is about 10)
At an angle 45deg, you get the 15kg displaced horizontally by 0.7m.
That would give a torque of 150*0.7 Nm
If the swing gets from zero to 45deg in 1.5 seconds, that equates to 1 revolution in 12 seconds, or 5 rpm. Or about 0.5 radians per second using the approximation of dividing by 10 for the conversion.
Power is thus 150*0.7*0.5 W
Or about 50W
Of course it isn't that simple.
The power required from standstill to 45deg varies depending on the angle - that's where the difference in your 24W and my 50W comes in.
And, if you went from 5RPM to zero instantly at 45deg, the baby just might not consider it a soothing experience.......
Levity aside, once moving I guess the swing would take power in a roughly sinusoidal manner, positive for the upwards swing and negative for the downward swing. Average power might not be much but the motor still has to provide peak torque and maximum RPM even if not simultaneously.