But their fears were unfounded. The false alarm was prompted by “balloons popping in the area,” according to Eddie L. Washington, a former Michigan State Police director who leads the school’s Department of Public Safety and Security.

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Such incidents have become periodic occurrences nationwide, fueled by Americans on heightened alert in the era of active shooter training and lockdown drills. The false alarms have been caused by a malfunctioning water heater at a North Carolina school, crushed bottles at a festival in New York City, and popping balloons at a Florida mall. Though they don’t involve gunfire, the incidents can spark stampedes and major police responses, causing trauma and, in some cases, injuries for the people who live through them.

On Saturday in Ann Arbor, Shivani Bhargava, a 19-year-old sophomore, hid in the library behind a makeshift barricade of tables and chairs with more than a dozen other students. When she heard footsteps, Bhargava thought: “This is it, the shooter is walking towards us.”

Even after students got the all clear, she said, that fear lingered.

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“I don’t feel safe going to the library anymore,” Bhargava said.

In San Francisco last month, a performance of the musical “Hamilton” devolved into chaos when people believed there had been a shooting. Authorities received multiple calls about an active shooter, said Lt. Jonathan Baxter, a spokesman for the San Francisco Fire Department. Three people were injured while fleeing, he said. One person had a heart attack and was saved by the quick actions of a bystander and a paramedic.

Last year in New York, a loud noise at a festival in Central Park attended by tens of thousands of people gave way to a panicked stampede. In August 2016, false alarms of gunfire set off frantic evacuations just weeks apart at international airports in New York and Los Angeles.

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The Los Angeles International Airport alarm came three years after a gunman actually opened fire there, killing a Transportation Security Administration officer and injuring three other people. For law enforcement, the potential of that type of danger looms over how they respond to worried calls.

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“If people are reporting a critical incident or being descriptive in terms of someone shooting, [saying] there’s an active shooter — especially since we’ve had something significant occur here in the past — we’re responding as if it’s real and preparing to deal with that particular threat,” said David L. Maggard Jr., chief of police at the Los Angeles and Van Nuys airports.

Sometimes these alarms end with injuries. Popping balloons sparked fears at the Florida Mall in Orlando in August 2016, sparking “mayhem” that ended with 10 people being treated at the mall and four taken to the hospital, according to Orange County Fire Rescue. Just two months earlier, the region had experienced a real deadly threat: a gunman killed 49 people at the Pulse nightclub about six miles from the mall.

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Lockdown procedures and the “run, hide, fight” tactics urged in Michigan’s alert have been drilled into minds of students and workers across the country. In some cases, that preparedness has saved lives.

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“Unfortunately, our young people, people at nightclubs, have learned that this may happen,” said Geoff Dean, then-sheriff of Ventura County, Calif., after that shooting. “They think about that. Fortunately, it probably saved a lot of lives that they fled the scene so rapidly.”

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A Washington Post analysis last year found that, during the 2017-2018 school year, more than 4.1 million students endured at least one lockdown , events that can overwhelm and terrify the young students worried about what lurks outside their classroom doors.

Experts said living through false alarms likely increases a person’s anxiety level. Joan Cook, an associate professor of psychiatry at the Yale School of Medicine, said she has not seen research on how false alarms specifically can affect people, but the fear of potentially imminent death is “an important moment that stays with you, oftentimes for life.”

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Even the way people at Michigan responded Saturday — mistaking popping balloons for gunshots — “suggests heightened anxiety,” said Jessica Stern, a research professor at Boston University and an expert in trauma and terrorism.

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“We’re all impacted, even when there’s an attack on the other side of the world,” she said. “Just the image of somebody doing something that terrible affects people. . . . I hear a loud noise and I put the thought of a gunshot out of my mind. The fact that I have to do that is interesting. The fact that I have to tell myself, ‘That’s a balloon.’ ”

Students at Northwestern University experienced this fear last year with a false report of a man with a gun on campus.

“It took away my ability to feel safe at Northwestern,” Karli Goldenberg, a 22-year-old senior at Northwestern, said a little more than a year later. “It just made me a more nervous person. It was a harsh reminder that even though it was a hoax, it very much could have been real.”

At the University of Michigan, school officials said authorities received up to 20 calls “reporting shots being fired” in Mason Hall, a stately 81-year-old building named for the state’s first governor. Leor Rosen, a 21-year-old sophomore, said she was at a vigil for the New Zealand victims when a campus police officer ran toward the crowd and shouted: “Run, move!”

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Washington, the school’s public safety and security director, said in an online message that he knew living through the false alarm was “a terrifying and traumatic experience.” He thanked people on the campus for how they reacted and emphasized that, despite the false alarm, officials still want people to report anything they think is suspicious or dangerous.