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Консультация № 200619
11.04.2021, 19:08
0.00 руб.
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1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Невесомая пружинка жесткости k одним концом прикреплена к стене, а другим – к бруску массы m, лежащему на горизонтальной поверхности. Вдоль поверхности на брусок действует гармоническая сила F= F0cos(ωt), которая вынуждает брусок колебаться с амплитудой А. Найдите массу бруска. Диссипативные силы в системе отсутствуют. Собственными колебаниями пренебречь.
F0 = 4 Н, k = 5 Н/м, А = 6 см, ω = 7 с–1.
а) 5,46 кг; б) 4,46 кг; в) 3,46 кг; г) 2,46 кг; д) 1,46 кг;
Невесомая пружинка жесткости k одним концом прикреплена к стене, а другим – к бруску массы m, лежащему на горизонтальной поверхности. Вдоль поверхности на брусок действует гармоническая сила F= F0cos(ωt), которая вынуждает брусок колебаться с амплитудой А. Найдите массу бруска. Диссипативные силы в системе отсутствуют. Собственными колебаниями пренебречь.
F0 = 4 Н, k = 5 Н/м, А = 6 см, ω = 7 с–1.
а) 5,46 кг; б) 4,46 кг; в) 3,46 кг; г) 2,46 кг; д) 1,46 кг;
Прикрепленные файлы:
Обсуждение
15.04.2021, 13:57
общий
это ответ
Здравствуйте, Дмитрий!
Для решения задачи воспользуемся указаниями здесь: Ссылка >>
Дано:
Н/м -- жёсткость невесомой пружины, прикреплённой к стене; 
Н -- гармоническая сила, действующая на брусок вдоль поверхности; 
м -- амплитуда вынужденных колебаний бруска.
Определить:
-- массу бруска, прикреплённого к пружине и лежащего на горизонтальной поверхности.
Поскольку диссипативные силы в системе отсутствуют, постольку отсутствует и затухание колебаний. А поскольку и собственными колебаниями можно пренебречь, постольку из формулы
получим
(кг).
Ответ:
кг.
Полученный ответ не совпадает ни с одним из предложенных Вами. Попробуем учесть собственные колебания. Их циклическая частота составляет
Тогда
откуда получим
Если
то 
что не имеет смысла. Если 
то 
(кг). Последний ответ совпадает с предложенным Вами вариантом д.
Для решения задачи воспользуемся указаниями здесь: Ссылка >>
Дано:
Н/м -- жёсткость невесомой пружины, прикреплённой к стене; Н -- гармоническая сила, действующая на брусок вдоль поверхности; м -- амплитуда вынужденных колебаний бруска.Определить:
-- массу бруска, прикреплённого к пружине и лежащего на горизонтальной поверхности.Решение
Поскольку диссипативные силы в системе отсутствуют, постольку отсутствует и затухание колебаний. А поскольку и собственными колебаниями можно пренебречь, постольку из формулы
получим (кг).Ответ:
кг.Полученный ответ не совпадает ни с одним из предложенных Вами. Попробуем учесть собственные колебания. Их циклическая частота составляет
Тогдаоткуда получим
Если
то что не имеет смысла. Если то (кг). Последний ответ совпадает с предложенным Вами вариантом д.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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