Final answer:
The Rolling Stones made their only deliberate excursion into Psychedelic Rock in 1967 with the album “Their Satanic Majesties Request”, influenced by the era's psychedelic culture and events like Woodstock.
Step-by-step explanation:
The Rolling Stones' only deliberate excursion into Psychedelic Rock was during the 1967 timeframe, notably with their album “Their Satanic Majesties Request”. This album was a marked departure from their traditional rock and blues style, seeking to embrace the psychedelic culture that was prominent at the time. The release was influenced by the success of The Beatles' "Sgt. Pepper's Lonely Hearts Club Band" and sought to experiment with new sounds and lyrical themes.
In 1969, while the Stones did not pivot to psychedelic rock, they were a part of the broader rock 'n' roll culture, which culminated in monumental events like Woodstock. This era was characterized by a youth movement that celebrated rebellion and individuality, with many festival-goers experimenting with psychedelic drugs. Hence, while the Rolling Stones themselves only made a brief foray into psychedelic rock, they were very much a part of the era that embraced its essence.