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# 7.34+ Consider the well-known problem of cart of mass m mnoving along the axis attached t0 spring (force constant k) whose other end is held fixed (Figure 5.2) . If...

## Question

###### 7.34+ Consider the well-known problem of cart of mass m mnoving along the axis attached t0 spring (force constant k) whose other end is held fixed (Figure 5.2) . If we ignore the mass of the spring (as we almost always do) then we know that the cart executes simple harmonic motion with angular frequency @ = Vkfm Using the Lagrangian approach, you can find the effect of the spring mass as follows: (a) Assuming that the spring is uniform and stretches uniformly: show that its kinetic energy is M;?

7.34+ Consider the well-known problem of cart of mass m mnoving along the axis attached t0 spring (force constant k) whose other end is held fixed (Figure 5.2) . If we ignore the mass of the spring (as we almost always do) then we know that the cart executes simple harmonic motion with angular frequency @ = Vkfm Using the Lagrangian approach, you can find the effect of the spring mass as follows: (a) Assuming that the spring is uniform and stretches uniformly: show that its kinetic energy is M;? , (As usual is the extension of the spring from its equilibrium length. Write down the Lagrangian for the system of cart plus spring: (Note: The potential energy is still ykx? ,) (6) Write down the Lagrange equation and show that the cart still executes SHM but with angular frequency Vk/(m 1 M/3); that is, the effeet of the spring mass M is just t0 add M/3 t0 the mass of the carl;

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