C12. (no numerical values needed) A spring mass with spring constant k oscillates in harmonic motion around the equilibrium position 0, viz. x(t) = A cos(wt). • a. What is the velocity v(t) and the acceleration a(t) of the spring mass? • b. Starting from Newton's 2nd law, show that w does NOT depend on the amplitude A. • c. What is the amplitude at given t in terms of x, v, and w ? (eliminate all trig. functions)
C12. (no numerical values needed) A spring mass with spring constant k oscillates in harmonic motion around the equilibrium position 0, viz. x(t) = A cos(wt). • a. What is the velocity v(t) and the acceleration a(t) of the spring mass? • b. Starting from Newton's 2nd law, show that w does NOT depend on the amplitude A. • c. What is the amplitude at given t in terms of x, v, and w ? (eliminate all trig. functions)
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Transcribed Image Text:C12. (no numerical values needed) A spring mass with spring constant k oscillates in
harmonic motion around the equilibrium position 0, viz. x(t) = A cos(uwt).
• a. What is the velocity v(t) and the acceleration a(t) of the spring mass?
• b. Starting from Newton's 2nd law, show that w does NOT depend on the
amplitude A.
• c. What is the amplitude at given t in terms of x, v, and w? (eliminate all trig.
functions)
Expert Solution
Step 1 (a)
The velocity and acceleration is given by
Step 2 (b)
From Newton's second law we have
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