11. A unit mass hangs in equilibrium from a spring with constant k = 1/16. Starting at t = 0, a force F(t) = 3 sint is applied to the mass. Find its displacement for t > 0.
11. A unit mass hangs in equilibrium from a spring with constant k = 1/16. Starting at t = 0, a force F(t) = 3 sint is applied to the mass. Find its displacement for t > 0.
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Transcribed Image Text:**Problem 11:**
A unit mass hangs in equilibrium from a spring with constant \( k = 1/16 \). Starting at \( t = 0 \), a force \( F(t) = 3 \sin t \) is applied to the mass. Find its displacement for \( t > 0 \).
**Problem 12: C/G**
A 4 lb weight stretches a spring 1 ft in equilibrium. An external force \( F(t) = 0.25 \sin 8t \) lb is applied to the weight, which is initially displaced 4 inches above equilibrium and given a downward velocity of 1 ft/s. Find and graph its displacement for \( t > 0 \).
**Problem 13:**
A 2 lb weight stretches a spring 6 inches in equilibrium. An external force \( F(t) = \sin 8t \) lb is applied to the weight, which is released from rest 2 inches below equilibrium. Find its displacement for \( t > 0 \).
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