Power and faithful love are both found in God. David worships as he is encouraged with this truth. God's power will care for His people. God's grace will lead that power as it is displayed. David takes comfort in this truth. By faith he worships, even as the circumstances of Psalm 62 make it clear that there was misunderstanding and attack coming to him from an enemy not mentioned by name (Psalm 62:3-4).
David was able to wait for God in silent worship, hoping in god because he knew that God was powerful and gracious. He knew God was his salvation (Psalm 62:6). He knew God was trustworthy and protective of His people (Psalm 62:8). God would vindicate David in due time. David simply kept himself worshiping and trusting the Lord.
And really, to worship God for His power and steadfast love is still my experience. The details of my life just happen to focus in on the gospel of Jesus Christ as the place where God's power meets His grace. Jesus has all power and authority given to Him by the Father. He can raise the dead, heal the sick, and most powerfully, save sinners like me! And Jesus IS steadfast love. He is the grace of God for us. While we were weak, while we were powerless and needy, while we were still sinners, while we were the enemies of God deserving His wrath, Jesus loved us and died for us! That is the power and grace of God shown on the cross and echoing in the defeat of death in His empty tomb!