If you are in a lift that starts to accelerate upward your feet would feel an increased push. When you stand on a train that starts to accelerate forward, you feel a force pushing you backwards. This is because of the law of inertia, Newton's first law. Every body stays in rest or keeps its initial velocity until the action of a force. If the lift or train accelerates, you need an extra force to accelerate together with it, and you feel it as a force equal to -ma, the product of your mass to the acceleration of your system, and pointing opposite direction as the acceleration.
The pendulum hangs from a support that starts to accelerate with 0.5 g. It is the same as if an extra force 0.5 mg acted on it in addition to the original mg force in the accelerating frame of reference, that is an increased gravity.
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