Emerging embedded systems deployed in the automotive and avionics domains execute applications with different criticalities, comprising what is known as Mixed Criticality Systems (MCS). Applications in MCS often share data between tasks (coming from sensors for instance). Data sharing is challenging because it can lead to increased response times or even unpredictable behaviors if not carefully addressed. Therefore, several prior works in MCS either assumed that tasks do not share data or disallowed it by design. Recent solutions attempt to mitigate the effects of data sharing, albeit by introducing new restrictions on the system either by prohibiting applications from caching shared data or prohibiting the operating system from running tasks with shared data in parallel. We find these solutions also to have limited applicability as they deteriorate system schedulability and prohibit simultaneous access to shared data. In this paper, we propose PENDULUM: a time-based cache coherence protocol to enable simultaneous and predictable access to shared data in MCS. Our evaluation shows that PENDULUM, achieves flexibility and better performance compared to existing solutions, while maintaining system predictability.