An eye-opening demonstration of trends in American politics is taking place in Berkeley, Calif. Berkeley--because of its Free Speech Movement in 1964, its People's Park Riots in 1969, and its recent flag burning after the invasion of Grenada--has been regarded as the center of modern American radicalism.

But some weeks ago, students at the University of California at Berkeley turned out in unusually large numbers to elect the first conservative dominated student government in 20 years.

Why? They say they were disenchanted with a student government that devoted the largest share of its time to national and international issues. The voters backed a self-proclaimed "moderate-conservative" party, which promised to focus on the local needs of students. A chief plank on the party's platform was the transformation of "People's Park" into an intramural athletic field with a softball diamond.

"People's Park" is a vacant lot three blocks from the Berkeley campus just off Telegraph Avenue. It has been owned by the University of California since 1967. In 1968, the university razed the buildings on the site with the intention of building either dormitories or playing fields. State money for construction was not then available, however, and the land stood unused. According to local lore, it was in April 1969 that community activists seized the idea of creating a "People's Park." They planted trees and flowers and put up a swing set. Street people began to use and even, some say, live on the property. On the morning of May 15, 1969, "Bloody Thursday," university officials evicted the squatters and hastily enclosed the site with an eight-foot fence.

Protest riots broke out that afternoon; one man was killed and another was blinded. When Gov. Ronald Reagan sent in the National Guard and the university faculty issued a call for negotiations, peace was restored. Then, in 1972, after the mining of Haiphong Harbor in North Vietnam, the students and townspeople tore down the fence.

Since then, the lot has been open. A few plantings were made, but essentially the place has been untended. Berkeley police cite it as a breeding ground for crime and a haven for the drug trade. In the town of Berkeley, however, there is strong pressure to leave the site undeveloped as a symbol of its citizenry's finest hours.

The town residents have become even more radical in recent years as Yumpies with a nostalgic bent reinforce aging activists' dreams. Berkeley citizens have sent tens of thousands of dollars to their "sister city" in a rebel-held area of El Salvador. Last year, they overwhelmingly approved a ballot initiative that banned electroshock treatment in the town. This year, another initiative would direct the mayor to ask the president and Congress to delete from U.S. aid to Israel the amount that country spends on settlements in occupied Arab territories. And opposing incumbent Rep. Ronald Dellums is Eldridge Cleaver, author of "Soul on Ice," born-again Christian, backed by Sun Myung Moon's Unification Church.

In town, radicals seem to be secure enough in power to continue to guide policy with or without student support. But at the university, students seem to be marching to a different drummer. In their recent election, the conservative United Campus Party captured four out of five executive offices and increased its representation in the Senate to 15 out of 30 seats. The radical Student Solidarity Coalition won only one executive office and held nine Senate seats. The balance of six Senate seats was won by the Science-Engineering Coalition and by independents.

So, is all settled at Berkeley?

Well, Berkeley's sandlot and swing-set politicians play by big league rules. To enforce campaign spending limits of $100 for executive offices and $50 for Senate seats, all candidates were required to submit detailed accounts of campaign expenditures. Amid murky allegations of United Campus Party overspending, a post-election investigation revealed falsifications. President-elect Michael Graveley, for example, was charged with negee paper-cutting services provided by Cleo's copy shop. Most touching was the failure of the United Campus campaign treasurer to submit her documents on time. She was at her Kappa Kappa Gamma sorority Mother-Daughter Day.

The student judicial committee found against the newly elected United Campus officials and disqualified them. They, in turn, filed suit to ensure their victory and claim their prize in the fall. Said Graveley, a friendly 20-year-old junior from San Leandro, Calif., "This is serious business. It's my professional career!"

The outcome of all this wrangling is not likely to be known until classes begin again in August, in the opinion of Allen Matthews, an editor at the Daily Californian. Meanwhile, across the bay in San Franciso, the big leaguers will be playing. All candidates might well note: stay away from Mother-Daughter banquets, and check your paper-cutting bills.