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Consider a solid uniform ball of mass M and radius Rrolling without slipping near the bottom of a frictionless hemispherical bowl of radius r as shown. r cos 0 r(1 – cos 0) The ball oscillates about the center of the fish bowl. Set the gravitational potential energy to be zero at the bottom of the bowl B. (4 points) Find the oscillation frequency of the ball. Hint: Since the ball is undergoing simple harmonic motion, x(t) (and hence v(t) follows a certain form. Also, since the energy of the system is conserved, then dE/dt = 0. Note: DO NOT use LaTeX codes when writing the expression. When typing Greek letters, just spell the name and DO NOT write backslashes, e.g. type alpha instead of \alpha.

Consider a solid uniform ball of mass M and radius Rrolling without slipping near the bottom of a frictionless hemispherical bowl of radius r as shown. r cos 0 r(1 – cos 0) The ball oscillates about the center of the fish bowl. Set the gravitational potential energy to be zero at the bottom of the bowl B. (4 points) Find the oscillation frequency of the ball. Hint: Since the ball is undergoing simple harmonic motion, x(t) (and hence v(t) follows a certain form. Also, since the energy of the system is conserved, then dE/dt = 0. Note: DO NOT use LaTeX codes when writing the expression. When typing Greek letters, just spell the name and DO NOT write backslashes, e.g. type alpha instead of \alpha.

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Consider a solid uniform ball of mass M and radius Rrolling without slipping near the bottom of a frictionless hemispherical bowl of radiusr as shown. r cos 0 r(1 - cos 0) The ball oscillates about the center of the fish bowl. Set the gravitational potential energy to be zero at the bottom of the bowl B. (4 points) Find the oscillation frequency of the ball. Hint: Since the ball is undergoing simple harmonic motion, x(t) (and hence v(t) follows a certain form. Also, since the energy of the system is conserved, then dE/dt = 0. Note: DO NOT use LaTeX codes when writing the expression. When typing Greek letters, just spell the name and DO NOT write backslashes, e.g. type alpha instead of \alpha.
Transcribed Image Text:Consider a solid uniform ball of mass M and radius Rrolling without slipping near the bottom of a frictionless hemispherical bowl of radiusr as shown. r cos 0 r(1 - cos 0) The ball oscillates about the center of the fish bowl. Set the gravitational potential energy to be zero at the bottom of the bowl B. (4 points) Find the oscillation frequency of the ball. Hint: Since the ball is undergoing simple harmonic motion, x(t) (and hence v(t) follows a certain form. Also, since the energy of the system is conserved, then dE/dt = 0. Note: DO NOT use LaTeX codes when writing the expression. When typing Greek letters, just spell the name and DO NOT write backslashes, e.g. type alpha instead of \alpha.
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