I wonder if someone could provide some guidance.

Im attempting to create a pendulum like behaviour in 2D space in Unity without using a hinge joint.

Essentially I want to affect a falling body to act as though it were restrained at the radius of a point, and to be subject to gravity and friction etc.

Ive tried many modifications of this code, and have come up with some cool 'strange-attractor' like behaviour but i cannot for the life of me create a realistic pendulum like action.

This is what I have so far:

    startingposition = transform.position;          //Get start position
    newposition = startingposition + velocity;      //add old velocity
    newposition.y -= gravity * Time.deltaTime;      //add gravity
    newposition = pivot + Vector2.ClampMagnitude(newposition-pivot,radius); //clamp body at radius???
    velocity = newposition-startingposition;        //Get new velocity
    transform.Translate (velocity * Time.deltaTime, Space.World);   //apply to transform

So im working out the new position based on the old velocity + gravity, then constraining it to a distance from a point, which is the element in the code i cannot get correct. Is this a logical way to go about it?