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You might be mistaken. I have never heard of a 'Psalm Sunday' - but there is a 'Palm Sunday' which is the Sunday before Easter Sunday. It is so called because the Gospel read that day in Christian churches concerns itself with how Jesus rode into Jerusalem and was greeted by people laying palm-leaves in his path.
Psalm 89.1-18
The psalm for the Mass on Corpus Christi (Sunday, 2 June 2013) is Psalm 110, verses 1-4 in the new numbering (it would be psalm 109 in the Vulgate).
On all Sundays and Solemnities (Christmas, All Saints, Immaculate Conception, Assumption, etc.) there are three (well, four if you count the psalm), usually an Old Testament reading, a psalm, a New Testament reading, and the Gospel. Weekday Masses only have one reading, the psalm, and the Gospel, there is no second reading on a non-solemnity.
Psalm 89.1-18
Psalm 9 is a lament Psalm.
The most quated psalm is psalm 23.
Psalm 23 is the most popular Psalm.
Psalm 91 has 16 verses and Psalm 100 has 5 verses. Psalm 91 is about how God protects us and Psalm 100 is about singing praises to the Lord.
99 - Psalm 1 - Psalm 99
The Psalm 92 is written when captive in Babylon.