Question

The figure below shows an old-style mechanical scale, used in butcher shops. As the cut of meat is placed in the tray, the needle (at the scale) will oscillate and finally settle down to indicate the weight. Lets ignore damping for the moment and focus on the undamped (frictionless) system. Lets assume that all of the components are massless; in other words, the item being weighed $m$ is far heavier than the other components. k m g k $L_3$ Scale Question 1 Using $\theta$, the angular rotation of the needle about its pin, as the generalized coordinate, derive the equation of motion for the needle. Assume all motion is small. Question 2 What is the natural frequency? One way to increase the stiffness of the system is to increase $k$. How else can the system's effective stiffness be increased? Explain this both mathematically and physically (i.e., in words!).

          The figure below shows an old-style mechanical scale, used in butcher shops. As the cut of meat
is placed in the tray, the needle (at the scale) will oscillate and finally settle down to indicate the
weight. Lets ignore damping for the moment and focus on the undamped (frictionless) system. Lets
assume that all of the components are massless; in other words, the item being weighed $m$ is far
heavier than the other components.
k
m
g
k
$L_3$
Scale
Question 1
Using $\theta$, the angular rotation of the needle about its pin, as the generalized coordinate, derive the
equation of motion for the needle. Assume all motion is small.
Question 2
What is the natural frequency? One way to increase the stiffness of the system is to increase $k$.
How else can the system's effective stiffness be increased? Explain this both mathematically and
physically (i.e., in words!).

The figure below shows an old-style mechanical scale, used in butcher shops. As the cut of meat
is placed in the tray, the needle (at the scale) will oscillate and finally settle down to indicate the
weight. Lets ignore damping for the moment and focus on the undamped (frictionless) system. Lets
assume that all of the components are massless; in other words, the item being weighed m is far
heavier than the other components.
k
m
g
k
L3
Scale
Question 1
Using θ, the angular rotation of the needle about its pin, as the generalized coordinate, derive the
equation of motion for the needle. Assume all motion is small.
Question 2
What is the natural frequency? One way to increase the stiffness of the system is to increase k.
How else can the system's effective stiffness be increased? Explain this both mathematically and
physically (i.e., in words!).

Added by Felipe T.

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