Bring a large pot of lightly salted water to a boil. Cook linguine at a boil until tender yet firm to the bite, about 11 minutes; drain.
Heat olive oil and butter in a saucepan over medium heat. Add shrimp, mushrooms, and garlic; cook and stir until fragrant, 1 to 2 minutes. Add artichokes, lemon juice, capers, and white wine. Cook and stir until shrimp is tender and contents are bubbling, about 10 minutes. Spoon shrimp piccata over individual beds of pasta. Season with salt and pepper.