In the figure, a solid cylinder M attached to a horizontal spring k (k = 3.00 N/m) rolls without 00000 slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these conditions the cylinder's center of mass executes simple harmonic motion with period 3M T = 2n. 2k where M is the cylinder mass. (Hint: Find the time derivative of the total mechanical energy.) (Halliday, Resnick & Walker, 2011)

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Chapter1: Units, Trigonometry. And Vectors
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In the figure, a solid cylinder
M
attached to a horizontal spring
k
(k = 3.00 N/m) rolls without
00000
slipping along a horizontal
surface. If the system is released
from rest when the spring is
stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational
kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show
that under these conditions the cylinder's center of mass executes simple harmonic
motion with period
3M
T = 2n.
2k
where M is the cylinder mass. (Hint: Find the time derivative of the total mechanical
energy.) (Halliday, Resnick & Walker, 2011)
Transcribed Image Text:In the figure, a solid cylinder M attached to a horizontal spring k (k = 3.00 N/m) rolls without 00000 slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) Show that under these conditions the cylinder's center of mass executes simple harmonic motion with period 3M T = 2n. 2k where M is the cylinder mass. (Hint: Find the time derivative of the total mechanical energy.) (Halliday, Resnick & Walker, 2011)
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