Physics questions?

Posted on 2015-11-23 07:40:00 in Chemistry by SIMON ROSE

A mass M is attached to a spring which has unstretched length L and spring constant k, and the spring has mass m which is uniformly distributed along the spring. The free end of the spring is attached to a horizontal frictionless surface and the mass is free to move along the direction of the spring.

a. Consider a short element of the spring of length dx at a distance r from the fixed end of the spring. When the mass M is moving with velocity v, what is the kinetic energy of this spring element?

b. What is the total kinetic energy of the spring at the moment when the mass M is moving with velocity v?

c. Does this system exhibit simple harmonic motion? If so, what is its frequency?

d. If instead of resting on a table, this spring and mass is hung from the ceiling and oscillates along the vertical direction. Does the system now exhibit simple harmonic motion? If so, what is its frequency?

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