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[Homework] Free body diagram for a system
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𝑚
𝐿𝜃
𝐹𝑅
𝑚𝑔
𝑚𝑔 cos𝜃
𝑚𝑔sin 𝜃
𝑚𝐿�̈�
𝑀 /𝐿𝑚
𝐿𝜃
𝐹𝑅
𝑚𝑔
𝑚𝑔 cos𝜃
𝑚𝑔sin 𝜃
𝑚𝐿�̈�
𝑀 /𝐿 𝑚
𝐿𝜃
𝐹𝑅
𝑚𝑔
𝑚𝑔 cos𝜃
𝑚𝑔sin 𝜃
𝑚𝐿�̈�
𝑀 /𝐿
𝑦
𝑥
𝑎𝐿
𝑐𝑎sin 𝜃
𝑏𝐿 𝜕sin 𝜃𝜕𝑡
𝑚𝑔sin 𝜃𝜃
𝑚𝐿23
𝑦
𝑥
𝑎𝐿
𝑐𝑎sin 𝜃
𝑏𝐿 𝜕sin 𝜃𝜕𝑡
𝑚𝑔sin 𝜃𝜃
𝑚𝐿23
𝑦
𝑥
𝑎𝐿
𝑐𝑎sin 𝜃
𝑏𝐿 𝜕sin 𝜃𝜕𝑡
𝑚𝑔sin 𝜃𝜃
𝑚𝐿23
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
𝑐 (𝑥− 𝑦 )
𝑏 ( �̇�− �̇� )
𝑊𝑔 �̈�
𝑥 𝑚𝑥
𝑐𝑥𝑑 �̇�2
𝑚�̈�
𝑃 (𝑡 )=𝑃0sinΩ𝑡
𝑊
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