"became sensible" is correct and can be used in written English.
You can use it to indicate that someone has thought more carefully or rationally about something. For example, "After talking with her friends, she became sensible about her decision to quit school".
So how did that unnamed footie title become Sensible Soccer?
The older you get, apparently, the more you abandon the daft socialist ideas of your youth to become sensible and conservative.
A single intuition of what it was like to be Marx, or Proust, or Gertrude Stein, or the ordinary man on the late-modern street, how they thought and how the world looked to them, is worth a thousand facts, for when we are equipped with the intuition every fact becomes sensible.
Maybe there is a point at which what you're saying becomes so indefensibly absurd that it meets up round the other side and becomes sensible?...And then more of this stuff about shaking up Washington, as if the current president was not a Republican.
However, this synchronization technique becomes sensible to high channel noise from a higher transmission rate of 115 kbps, limiting the use of the ZigBee and Wireless Fidelity (Wi-Fi) protocols which permit wireless transmissions up to 250 kbps and 65 Mbps [25, 26], respectively.
However, once calibrated, it becomes sensible to compare the search results from different laboratories using different machines and different analysis software.
However, once the calibration is done for each laboratory, it becomes sensible to compare the search results obtained at different laboratories.
With his small joke, the stupidest of all ideas became reasonable, even almost sensible, maybe even genius.
"The deal's original terms became less sensible when we recognized Global Crossing was having some serious difficulties," Michael J. Small, chief executive of Centennial, said in an interview.
For those people who had an urgent need to access electricity, the acquisition of a new backup device (engine-generator) became a sensible option.
