Undamped Harmonic Oscillator for a Swing

Question

I managed to arrive at the equation of an undamped harmonic oscillator which is $$\frac{t\sin\omega_1}{2\omega_1}$$ where $\omega_1$ is the frequency of the driving force as it approaches the natural frequency which I compute as $\sqrt\frac{g}{l}$ where g is the gravitational force and l is the length of the swing, my question is how can I put a constraint on the driving/angular frequency so that the swing does not go over $\frac{+}{-}\frac{\pi}{2}$ would be great if you point me in the direction where I could read further about how it works. Thanks.