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# J-sol - Chapter J Problems Blinn College Physics 2425 Terry...

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Chapter J - Problems Blinn College - Physics 2425 - Terry Honan Problem J.1 The position as a function of time for a particle in simple harmonic motion is x H t L = H 4 cm L cos AI 3 p s - 1 M t +p E . (a) What are the period and frequency? (b) What is the amplitude of the oscillation? (c) What is the phase angle? (d) What is the maximum speed and maximum acceleration? (e) At t = 0.25 s what is the position of the particle? (f) Suppose this describes the postion of a 0.6 kg mass at the end of a spring. What is the spring constant? Solution to J.1 The general form for simple harmonic motion is x H t L = A cos H w t +f L . Here we have x H t L = H 4 cm L cos AI 3 p s - 1 M t +p M ï A = 4 cm , w = 3 p rad s and f = p (a) T = 2 p w = 2 3 s and f = w 2 p = 1.5 Hz (b) A = 4 cm (c) v max = w A = 3 p H 0.04 L = 0, 377 m ê s and a max = w 2 A = H 3 p L 2 0.04 = 3.55 m ë s 2 (d) f = p (e) x H 0.25 s L = 4 cos H 3 p μ 0.25 + p L = 2.83 cm (Note that your calculator must be in the radians mode to evaluate the above expression.) (f) For a mass/spring system: w = k m ï k = m w 2 = 53.3 N ê m Problem J.2 When a mass is hung from a spring is stretches it by 15 cm. What is the period of the oscillations of this system?

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J-sol - Chapter J Problems Blinn College Physics 2425 Terry...

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