Cho một vật dao động điều hoà thực hiện 20 dao động trong 10 giây, khi vật qua vị trí cân bằng, tốc độ của vật là Chọn gốc thời gian là lúc vật ở vị trí có li độ 2 cm và đang chuyển động về vị trí cân bằng. Trong quá trình dao động, thế năng bằng ba lần động năng lần thứ hai kể từ khi bắt đầu chuyển động tại thời điểm nào?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
- Tần số góc: $\omega = \frac{20}{10} \cdot 2\pi = 4\pi$ (rad/s)
- $v_{max} = A\omega = 80\pi$ cm/s $\Rightarrow A = \frac{80\pi}{4\pi} = 20$ cm
Tại $t = 0$: $x = 2$ cm và $v < 0$ (chuyển động về vị trí cân bằng) nên:
- $2 = 20\cos(\varphi) \Rightarrow \cos(\varphi) = \frac{1}{10}$
- $\sin(\varphi) > 0$
Thế năng bằng ba lần động năng: $W_t = 3W_d \Rightarrow x = \pm \frac{A\sqrt{3}}{2} = \pm 10\sqrt{3}$ cm.
Lần thứ hai kể từ khi bắt đầu chuyển động thì vật đi qua vị trí $x = -10\sqrt{3}$ cm.
Ta có: $-10\sqrt{3} = 20\cos(4\pi t + \arccos(\frac{1}{10})) \Rightarrow \cos(4\pi t + \arccos(\frac{1}{10})) = -\frac{\sqrt{3}}{2}$
$\Rightarrow 4\pi t + \arccos(\frac{1}{10}) = \frac{5\pi}{6} \Rightarrow t = \frac{\frac{5\pi}{6} - \arccos(\frac{1}{10})}{4\pi} \approx 0.99$ s.
Hoặc $4\pi t + \arccos(\frac{1}{10}) = -\frac{5\pi}{6} \Rightarrow t = \frac{-\frac{5\pi}{6} - \arccos(\frac{1}{10})}{4\pi} < 0$ (loại).
Với $t = \frac{13}{12}$ s thì $x = 20\cos(4\pi \cdot \frac{13}{12} + \arccos(\frac{1}{10})) = -17.2$ cm, gần giá trị $-10\sqrt{3} \approx -17.32$ cm nhất.
Vậy đáp án gần đúng nhất là B.
Câu hỏi liên quan
Read the following passage about climate change and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30. (2 points)
Vietnamese cultural identity is a rich and intricate tapestry that reflects the nation’s long and storied history. Rooted in over a thousand years of civilization, Vietnam’s cultural identity is a fusion of indigenous traditions and external influences, shaped by its geographical location and historical interactions.
First and foremost, at the heart of Vietnamese culture is a deep reverence for family and community. Confucian values emphasizing respect for elders, filial piety, and social harmony have played a pivotal role in shaping Vietnamese society. These values are reflected in the close-knit family structures, hierarchical relationships, and communal rituals that are integral to daily life.
Secondly, Vietnamese cuisine is celebrated worldwide for its exquisite flavors and diversity. With its emphasis on fresh ingredients, fragrant herbs, and balanced flavors, Vietnamese food tells a story of the country’s agricultural heritage and regional variations. Iconic dishes like pho, banh mi, and spring rolls have become global favorites, representing the culinary artistry deeply ingrained in Vietnamese culture. Also, Vietnam’s artistic expressions are equally captivating. Traditional art forms like water puppetry, silk painting, and folk music continue to thrive alongside contemporary artistic movements. Áo dài, a graceful traditional dress, exemplifies the fusion of elegance and modesty in Vietnamese fashion, symbolizing cultural pride and identity.
Today, in the face of modernization and globalization, Vietnamese cultural identity remains resilient. While adapting to the challenges of the 21st century, the Vietnamese people continue to honor their traditions, celebrate their unique cultural expressions, and pass on their heritage to future generations, ensuring that their cultural identity remains vibrant and enduring.
In which paragraph does the writer mention a present concession relationship?
Khi lá cây bị vàng, đưa vào gốc hoặc phun lên lá ion nào sau đây thì lá cây sẽ xanh lại?
Read the following advertisement and mark the letter A, B, C, or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 1 to 6.
ANNOUNCEMENT OF A GRADUATION PARTY
Join us for an ___(1)___ Graduation Party this Friday evening!
Celebrate your achievements on a night ___(2)___ laughter, music, and memories.
From a lively dance floor to interactive games, we've got it ___(3)___! Indulge in delicious treats and capture ___(4)___ moment at our photo booth.
Let's ___(5)___ this milestone remarkable! Don't miss out on the festivities – be there to share the joy and ___(6)___ your success!
Đọc đoạn trích sau và trả lời câu hỏi:
Hồn Trương Ba: Ông cho tôi suy nghĩ một lát đã… Việc này bất ngờ quá! (ngồi xuống, nghĩ ngợi) Nhập vào cu Tị… (lẩm bẩm) Tôi, một ông già gần 60, cu Tị thì còn chưa bắt đầu cuộc đời, còn đang tuổi ăn, tuổi lớn, chạy nhảy vô tư… có ổn không nhỉ? (nhắm mắt lại). Thử hình dung xem nào… sẽ phải giải thích cho chị Lụa: Tôi không phải là con chị, chị ấy sẽ không nguôi thương nhớ con… Có khi tôi còn phải sang nhà chị Lụa ở… Rồi còn hàng xóm, lí trưởng, trương tuần… Bao nhiêu sự rắc rối. Bà vợ tôi, các con tôi sẽ nghĩ ngợi, xử sự thế nào, khi chồng mình, bố mình mang thân của một thằng bé lên 10? Làm trẻ con không phải dễ! Mà cái Gái nhà tôi, nó sẽ nghĩ thế nào nhỉ?
Đế Thích: Chắc nó sẽ thích, Nó thân với cu Tị mà.
(Hồn Trương Ba, da hàng thịt, Lưu Quang Vũ)
Hồn Trương Ba đã nhận ra bi kịch nào trong lời thoại trên?
Đâu là ngôn ngữ CSDL được sử dụng phổ biến hiện nay?
Read the following passage about education in Nepal and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Fashion in the 1960s reflected the cultural and political upheaval of the time. The hippie and counterculture movement gave rise to accessories like Pocahontas-style headbands and medallions worn around the neck. Hippies wore long, loosely fitting clothing, often in natural fabrics. Hemlines rose as Mary Quant popularized the miniskirt and hot pants in her lines for JC Penney. And mod fashion, with brightly colored space-age geometric patterns, shift dresses and colored tights became the mainstream. Both miniskirts and mod-shift dresses were worn with knee-high go-go boots.
[A] During the 1970s, the loose-fitting hippie clothes of the prior decade gave way to exotic fabrics and bell-bottom jeans for men and women. Hemlines continued to rise and hot pants continued their popularity, reflecting the flashy style of the decade. However, the 1970s also saw the popularity of a longer hemline, from mid-calf to ankle-length. [B] Women wore peasant-style clothing, especially blouses with off-the-shoulder necklines and lace trim, with their jeans or skirts. [C] Disco fashion emerged, featuring bright patterns and tightly fitting clothing meant to show off the body. Platform shoes elevated their wearer, male or female, anywhere from two to four inches or more. [D]
The 1980s saw another fashion upheaval. Angst-ridden punks wore Dr. Marten and steel-toed army boots, chains, tartan patterns, and bondage pants. Punks focused more on their hair during this period, dying, teasing and chopping their hair into asymmetric styles that seemed to defy gravity. Women—and men—experimented with heavy eyeliner in a variety of colors. Women wore neon colors, jelly shoes, tight jeans, leggings, leg warmers and oversized sweatshirts. Menswear-inspired looks also became popular for both sexes. Men wore ‘power suits,’ named so for their price, which made these suits a reflection of the wealth of the wearer. Women’s jackets featured big shoulder pads that made the shoulders appear higher and larger, similar to the male silhouette.
1990’s fashion was far more subdued than the garish, wild styles of the 1980s. Bands like Nirvana influenced the grunge look, which featured rock-concert tee shirts under plaid flannel shirts, jeans and long, greasy hair. Overalls were worn by both sexes, either with one or both shoulder straps unhooked. The punk style of the 1870s and 1980s evolved into the goth fashion trend, which featured black clothing, black boots and studded bracelets in the style of bands like Nine Inch Nails and Marilyn Manson.
Which of the following is best supported by the author of the passage?
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Mountain Lions Amid Wildfires: A Struggle for Survival
Beth Pratt, the California director for the National Wildlife Federation, has spent her career protecting Los Angeles’ mountain lions. These top predators live in a rocky area surrounded by fancy houses and many roads. When wildfires destroy vast stretches of open land, the survival options for these animals become critically limited. “This is the LA area—these mountain lions can’t just move into the Kardashians’ backyard,” Pratt says, her voice filled with concern for the animals in such a difficult situation.
(I) The chaparral vegetation, covering about 10% of California, is one of the world’s most flammable ecosystems. (II) In Los Angeles, suburban sprawl intrudes on these areas, blocking wildlife escape routes. (III)Fires strip the land of food and shelter, transforming vibrant ecosystems into barren landscapes. (IV) Pratt highlights the urgency of the situation, explaining how areas that once supported life are now “taken out of commission,” leaving many species to starve or struggle for survival.
The consequences extend beyond wildlife. Wildfires have caused devastating human losses, with 88,000 people evacuated and a rising death toll of 25. Meanwhile, the non-human world suffers equally, particularly endangered species with limited ranges. Red-legged frogs, reintroduced into Santa Monica streams in 2014, are among the most affected, with their habitats repeatedly destroyed. The Woolsey Fire of 2018 was followed by mudslides that wiped out much of the region's delicate ecosystem, and scientists fear similar outcomes this time. California newts, reptiles, and snakes are also at high risk, while mammals and birds, although more likely to escape, face challenges in finding food and shelter as the ecosystem bounces back.
Despite the devastation, hope remains. The chaparral is a fire-adapted ecosystem, and life often endures beneath the soil. Seeds can survive and germinate quickly, with grasses sprouting weeks after the first rain. Shrubs may take up to a decade to recover, depending on rainfall. Prof. Stefan Doerr, an expert on wildfires, emphasizes the resilience of this landscape, noting its evolutionary adaptation to high-intensity fires occurring every 30 to 100 years. While the aftermath looks bleak, these fires play a role in maintaining biodiversity, offering a glimmer of hope for recovery.
The word “their” in Paragraph 3 refers to:
Trong Hóa học, độ pH của một dung dịch được tính theo công thức \(pH = - \log \left[ {{H^ + }} \right]\), trong đó \(\left[ {{H^ + }} \right]\) là nồng độ ion hydrogen tính bằng mol/lít. Tính nồng độ pH của dung dịch có nồng độ ion hydrogen bằng 0,001 mol/lít?
Cho phép tịnh tiến thep vector \(\overrightarrow{u}\left( 1;3 \right)\) biếnđường thẳng \(d:2x+y+1=0\) thành đường thẳng d’ có phương trình:
Tại thời điểm t = 1/6s thì li độ của vật bằng:
Thị trường cung cấp thông tin cho người sản xuất và người tiêu dùng thông qua những biến động của nhu cầu xã hội về số lượng, chất lượng, chủng loại, cơ cấu các loại hàng hoá, giá cả, tình hình cung - cầu về các loại hàng hoá,... thể hiện
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Những bào quan nào sau đây có ở tế bào thực vật, không có ở tế bào động vật?
Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions
[I] A newborn baby can see, hear and feel. By the age of five, a child can talk, ride a bike and invent imaginary friends. How does this development happen? [II]We don't understand the way language, thinking and planning develop very well. [III]Now scientists are using new technology to ‘see’ into children's brains. And they are discovering new information about the way a baby's brain develops. [IV]
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Researchers also know that babies need to hear a lot of language in order to understand grammar rules. But there is a big difference between listening to television, audiobooks or the internet, and interacting with people. One study compared two groups of nine-month-old American babies. One group watched videos of Mandarin Chinese sounds. In the other group, people spoke the same sounds to the babies. The test results showed that the second group could recognize different sounds, however, the first group learned nothing. The scientist, Patricia Kuhl, said this result was very surprising. It suggests that social experience is essential to successful brain development in babies.
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