The figures shows a overhead view (they are lying on the ground without any friction) long uniform rod of mass 0.600 kg is free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant k =1850 N/m is connected horizontally between one end of the rod and a fixed wall. When the rod is in equilibrium, it is parallel to the wall. (a) Indicate all forces acting on the rod (b) Find the torque for a small displacement from the equilibrium position (use small angle approximation) (c) Show that the resulting motion is a simple harmonic oscillation and find its period. (d) Suppose you did the experiment and found that the amplitude of the oscillation decays exponentially as Exp[-bt] where b is a constant. Indicate what kind of forces could make sense of your observation and write down a Newton’s equation for it
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
The figures shows a overhead view (they are lying on
the ground without any friction) long uniform rod of mass 0.600 kg
is free to rotate in a horizontal plane about a vertical axis through its
center. A spring with force constant k =1850 N/m is connected
horizontally between one end of the rod and a fixed wall. When the
rod is in equilibrium, it is parallel to the wall.
(a) Indicate all forces acting on the rod
(b) Find the torque for a small displacement from the
equilibrium position (use small angle approximation)
(c) Show that the resulting motion is a simple harmonic
oscillation and find its period.
(d) Suppose you did the experiment and found that the
amplitude of the oscillation decays exponentially as Exp[-bt]
where b is a constant. Indicate what kind of forces could
make sense of your observation and write down a Newton’s
equation for it.
![Problem 7. The figures shows a overhead view (they are lying on
the ground without any friction) long uniform rod of mass 0.600 kg
is free to rotate in a horizontal plane about a vertical axis through its
center. A spring with force constant k=1850 N/m is connected
horizontally between one end of the rod and a fixed wall. When the
rod is in equilibrium, it is parallel to the wall.
(a) Indicate all forces acting on the rod
(b)
Find the torque for a small displacement from the
equilibrium position (use small angle approximation)
Show that the resulting motion is a simple harmonic
oscillation and find its period.
(c)
(d)
Suppose you did the experiment and found that the
amplitude of the oscillation decays exponentially as Exp[-bt]
where b is a constant. Indicate what kind of forces could
make sense of your observation and write down a Newton's
equation for it.
Wall
10000
Rotation axis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ee03a02-1de5-4580-8c03-88e6a0589671%2Fe1467fb2-3715-4e8c-9ba1-43226d90f4a7%2Fnumx6gh_processed.jpeg&w=3840&q=75)
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