Here is a Hymn Based on Psalm 60: O God, Thou Hast Rejected Us

"(To the chief Musician upon Shushaneduth, Michtam of David, to teach; when he strove with Aramnaharaim and with Aramzobah, when Joab returned, and smote of Edom in the valley of salt twelve thousand.) O God, thou hast cast us off, thou hast scattered us, thou hast been displeased; O turn thyself to us again. Thou hast made the earth to tremble; thou hast broken it: heal the breaches thereof; for it shaketh. Thou hast shewed thy people hard things: thou hast made us to drink the wine of astonishment. Thou hast given a banner to them that fear thee, that it may be displayed because of the truth. Selah. That thy beloved may be delivered; save with thy right hand, and hear me. God hath spoken in his holiness; I will rejoice, I will divide Shechem, and mete out the valley of Succoth. Gilead is mine, and Manasseh is mine; Ephraim also is the strength of mine head; Judah is my lawgiver; Moab is my washpot; over Edom will I cast out my shoe: Philistia, triumph thou because of me. Who will bring me into the strong city? who will lead me into Edom? Wilt not thou, O God, which hadst cast us off? and thou, O God, which didst not go out with our armies? Give us help from trouble: for vain is the help of man. Through God we shall do valiantly: for he it is that shall tread down our enemies."

Here is another hymn based on Psalm 60: O God, Thou Hast Rejected Us

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Earlier Posts on the Psalms: 

• That Man is Blest (Psalm 1)
• On the Good and Faithful (Psalm 4)  
• Lord, Our Lord Thy Glorious Name (Psalm 8)
• Wholehearted Thanksgiving to Thee I Will Bring (Psalm 9) 
• In God Will I Trust. (Psalm 11) You may recognize this melody from other hymns, like How Firm a Foundation.
• Who, O Lord, With Thee Abiding (Psalm 15)
• When in the Night I Meditate (Psalm 16)
• Psalm 19: The Spacious Heavens Declare (Psalm 19)
• Amid the Thronging Worshippers (Psalm 22) 
• The Lord's My Shepherd, I'll Not Want (Psalm 23)
• Jehovah is My Light (Psalm 27)
• Now Unto Jehovah Ye Sons of the Mighty (Psalm 29)
• O Lord by Thee Delivered (Psalm 30)
• How Blest is He Whose Tresspass (Psalm 32)
• Ye Children, Come, Give Ear to Me (Psalm 34)
• Be Thou My Helper in the Strife (Psalm 35)
• Thy Mercy and Thy Truth, O Lord (Psalm 36)
• In Thy Wrath and Hot Displeasure (Psalm 38)
• A Mighty Fortress is Our God (Psalm 46)
• Within Thy Temple, Lord (Psalm 48)
• The Mighty God, Jehovah Speaks (Psalm 50)
• God Be Merciful to Me (Psalm 51)
• Gracious God, Our Hearts Renew (Psalm 51)
• O God, the God That Saveth Me (Psalm 51)
• Jehovah to My Prayer Give Ear (Psalm 55)
• O God, Be Merciful, Be Merciful to Me (Psalm 56)
• Do Ye, O God, Speak Righteousness (Psalm 57)
• Do Ye, O God, Speak Righteousness (Psalm 58)