Question

Derive the differential equation of motion of free vibration for the bar shown in figure in terms of the angular displacement ($\theta$) about 'o' and find the natural frequency of oscillation. The bar is massless with an end mass 'm' attached. It has a length of 3a and is supported on spring and damper as shown. Note: Use Newton's 2$^{nd}$ law to derive the equation of motion.

          Derive the differential equation of motion of free vibration for the bar shown
in figure in terms of the angular displacement ($\theta$) about 'o' and find the natural
frequency of oscillation. The bar is massless with an end mass 'm' attached. It
has a length of 3a and is supported on spring and damper as shown.
Note: Use Newton's 2$^{nd}$ law to derive the equation of motion.

Derive the differential equation of motion of free vibration for the bar shown
in figure in terms of the angular displacement (θ) about 'o' and find the natural
frequency of oscillation. The bar is massless with an end mass 'm' attached. It
has a length of 3a and is supported on spring and damper as shown.
Note: Use Newton's 2^nd law to derive the equation of motion.

Added by Carla P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Krystal K

Step 1

Start by considering the forces acting on the mass m' at the end of the bar. There are three forces: the gravitational force mg acting downwards, the spring force kθ acting upwards, and the damping force c(dθ/dt) acting in the opposite direction of the velocity. Show more…

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Derive the differential equation of motion of free vibration for the bar shown in the figure in terms of the angular displacement (Î¸) about the origin (o') and find the natural frequency of oscillation. The bar is massless with an end mass m' attached. It has a length of 3a and is supported by a spring and damper as shown. Note: Use Newton's 2nd law to derive the equation of motion.