Learn Hardcore Japanese: kesa tiisana zisin de dentyuu ga sukosi yuremasita. - This morning the utility pole shook a little because of a small earthquake.

今朝 is acting as a time‐adverbial, so no particle is needed. In Japanese, many time expressions (like 今朝, 昨日, 来週) can stand alone before the verb to mean “this morning,” “yesterday,” “next week,” etc. You could add に (今朝に), but that’s less common in everyday speech.

What does the で in 小さな地震で indicate? Couldn’t it be 地震に?

Here, で marks the cause (“due to the small earthquake”).

地震で電柱が揺れた = The pole swayed because of the earthquake.
Using に would be incorrect for cause (に often marks time or indirect objects). If you wanted a more formal “by” or “due to,” you could say 地震によって.

Why is 小さな used instead of 小さい before 地震?

小さな is a special 連体形 (attributive form) that only appears before nouns, just like 大きな. It sounds a bit more literary or natural when directly modifying a noun.

Casual: 小さい地震
Polished/written: 小さな地震

Why is 電柱 marked with が rather than を or は?

The verb 揺れる is intransitive (the subject itself shakes). So the thing shaking—電柱—gets the subject marker が.

If you said 電柱を揺らした, that would mean “(someone) shook the utility pole” (using the transitive 揺らす).
You could use は instead of が (電柱は少し揺れました), but that would make “utility pole” the topic rather than marking it neutrally as the subject.

How does 少し function in this sentence?

少し is an adverb meaning “a little” or “slightly.” It modifies the verb 揺れました, telling us how much the pole swayed. In Japanese, adverbs usually come right before the verb or between the subject and verb.

What’s the difference between 揺れる and 揺らす?

揺れる (intransitive): “to shake” or “to sway” on its own or by an external force.
揺らす (transitive): “to shake” or “to rock” something intentionally.
Since the pole moved due to the earthquake (not someone shaking it), we use 揺れる.

Why is the verb in the polite past form (揺れました) instead of the plain past (揺れた)?

揺れました is polite past (です/ます‐style), common in conversations with coworkers, customers, or in more formal contexts. In casual speech with close friends or family, you could say 揺れた.

Could I rephrase this as 今朝、小さな地震があって電柱が少し揺れました? What’s the nuance?

Yes, that’s perfectly natural. Here you split it into two clauses:
1) 小さな地震があって (“there was a small earthquake”),
2) 電柱が少し揺れました (“the pole swayed a little”).
The original 地震で condenses the cause‐effect into one phrase (“because of the earthquake…”). Your version simply makes the earthquake occurrence more explicit before stating its result. Both are correct.