Here's my problem diagram:
I am working on a hobby project in which a motor is required to rotate a pulley that is connected to a pendulum as shown in the image. The maximum torque, Horsepower and RPM ratings of the motor are to be determined so that it can move the pendulum object of mass $m$ for a distance of $L$ and height $h$. The rivet on the pulley is at a distance $d$ from the equilibrium position of the pendulum.
This is my attempt so far.
Force required by the pulley, $$F = m * a$$ Torque, $$T = F * r $$
Where I am stuck - how to calculate a??
Once I get the Torque, I know how to calculate the Horsepower.