Block and hemispherical surface as function of theta

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Reference no: EM133317305

A small block of mass m slides from rest at point A on the inner surface if a smooth hemispherical surface of radius R.

1. Write down the Lagrangian function of the system using r and theta as generalized coordinates.

2. Using the constant equation r - R = 0 and Lagrange multiplier lambda, write down the Lagrange equations of motion for r and theta.

3. Find the angular speed and magnitude of the force between the block and the hemispherical surface as a function of theta.

4. Find the frequency of small oscillations of the block.

Reference no: EM133317305

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