Write down the Equation of Motion and the angular frequency of oscillation. A so

Question

Write down the Equation of Motion and the angular frequency of

oscillation.

A solid cylinder (mass M, radius R) attached to a horizontal spring (spring constant k) rolls without slipping along a horizontal surface. The moment of inertia with respect to the center of the cylinder is I = MR2/2. The kinetic energy of the cylinder is T = 1/2 M x.2 + 1/2 I phi. 2, where x is the position of the center of mass relative to the equilibrium position of the spring and phi measures the rotation of the cylinder.

Explanation / Answer

T=1/2mv2+1/2I2

=v/r,I=mr2/2

T=3/4mv2

3/4mv2+1/2kx2=constant:conservation of energy

comparing with:v2+2x2=constant

2=2k/3m

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