Sara var tydligen också tvungen att stanna hemma efter samma olycka.

Var is the past tense of är.
So Sara var ... tvungen att ... means Sara was ... forced/obliged to ... or Sara had to ... in the past.

The basic pattern is:

• är tvungen att = has to / is forced to
• var tvungen att = had to / was forced to

So the sentence is talking about a past situation.

Tydligen usually means apparently, evidently, or it seems.

It often shows that the speaker is not stating something as direct personal knowledge, but as something they have understood from other information, reports, or context.

So:

• Sara var tydligen också tvungen att stanna hemma ...

suggests something like:

• Apparently, Sara also had to stay home ...

It adds a slight sense of inference or second-hand information.

This is mainly because of normal Swedish word order in a main clause.

In Swedish main clauses, the finite verb usually comes in the second position. That is the famous V2 pattern. Here the finite verb is var.

The sentence structure is roughly:

• Sara = subject
• var = finite verb
• tydligen också = sentence adverbs
• tvungen att stanna hemma ... = rest of the predicate

So this order is natural:

• Sara var tydligen också tvungen att stanna hemma ...

A learner-friendly way to think of it is: after the subject and finite verb, Swedish often places words like tydligen, också, inte, etc. before the main adjective, participle, or infinitive phrase.

Tvungen att means forced to, obliged to, or more naturally in many contexts, had to.

It is a very common Swedish structure:

• vara tvungen att + infinitive

Examples:

• Jag är tvungen att gå. = I have to leave.
• Hon var tvungen att vänta. = She had to wait.

In your sentence:

• var tvungen att stanna hemma = had to stay home

Even though tvungen originally relates to being compelled or forced, in everyday Swedish this expression is often just the normal way to say had to in the past.

Because tvungen agrees with Sara, which is a singular common-gender noun/person.

The forms are:

• tvungen = common gender singular
• tvunget = neuter singular
• tvungna = plural

Examples:

• Sara var tvungen att gå.
• Barnet var tvunget att gå.
• De var tvungna att gå.

So in this sentence, tvungen matches Sara.

Because tvungen is followed by the pattern att + infinitive.

So:

• tvungen att stanna
• tvungen att vänta
• tvungen att åka

This is simply how the construction works in Swedish.

Compare:

• Hon var tvungen att läsa. = She had to read.

You should learn vara tvungen att as one unit.

Stanna hemma is the normal idiomatic way to say stay home or stay at home.

Swedish often uses hemma without a preposition in this kind of expression.

Compare:

• Jag är hemma. = I am at home.
• Hon stannade hemma. = She stayed home / stayed at home.

Using something like i hemmet would sound much more formal, unusual, or like you are talking about the home as an institution or environment, not just the ordinary idea of being at home.

Here efter means after, and it introduces a noun phrase:

• efter samma olycka = after the same accident

It tells you what event happened before Sara had to stay home.

So the structure is:

• efter
  • noun phrase
• efter samma olycka

This is completely normal Swedish.

Because samma works as a determiner here, and Swedish normally says:

• samma bok = the same book
• samma dag = the same day
• samma olycka = the same accident

You usually do not add an article when samma is used this way.

So:

• samma olycka = correct
• den samma olyckan = possible only in special, more emphatic or formal styles, but not the normal everyday choice here

For a learner, the safest rule is: use samma + noun.

Usually, no. Samma is convenient because it normally stays the same.

Examples:

• samma bil = the same car
• samma hus = the same house
• samma böcker = the same books

So in your sentence, samma olycka follows the normal pattern.

Yes, but that would usually mean Sara has to stay home in the present or near future, not the past.

Your sentence uses var tvungen att, which is the normal way to express had to in the past:

• Sara var tvungen att stanna hemma. = Sara had to stay home.

If you say:

• Sara måste stanna hemma.

that usually means:

• Sara must stay home / has to stay home

So var tvungen att is the right choice for a past event.

Tydligen också is the more natural order here.

Both tydligen and också are adverb-like words, but they do not always sound equally natural in every position. In this sentence, tydligen också flows better and is what you would most likely hear.

Very roughly:

• tydligen comments on the whole statement: apparently
• också adds the meaning also

So tydligen också naturally gives:

• apparently also

If you reversed them, the sentence might still be understandable, but it would sound less natural in ordinary Swedish.

A useful breakdown is:

• Sara = Sara
• var = was
• tydligen = apparently
• också = also
• tvungen att = forced to / had to
• stanna hemma = stay home / stay at home
• efter = after
• samma olycka = the same accident

So grammatically the core is:

• Sara var tvungen att stanna hemma.

Then Swedish adds:

• tydligen for apparently
• också for also
• efter samma olycka for the time/cause context

That makes the full sentence feel very natural and compact in Swedish.