How does the pendulum affect the cart?

The swinging bob exerts a centrifugal force on the cart proportional to angular velocity squared times sine of the angle. This couples the two degrees of freedom so energy flows between cart spring and pendulum gravity.

What happens with no spring?

Without a spring the total horizontal momentum of the cart plus bob is conserved. The cart drifts in the opposite direction of the bob swing. This is like a person walking on a floating platform.

Cart + Pendulum Simulator — Coupled Dynamics

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Cart + Pendulum