In literature and in writing it's important to understand the subject and the theme and also be able to identify key points and create your own opinion. When analyzing a story, you need to discuss the following elements:
- Setting
- Mood
- Main Charecters
- Main conflicts
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The expression "her heart was throbbing" implies that her heart was ultimately beating or pounding. It is to beat rapidly or violently. In simpler words, it just means that her heart was beating fast due to an emotional outburst. Hope this answers your question. Have a great day!