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.
While driving behind a car traveling at 3.00 m/s, you notice that one of the car’s tires has a small hemispherical bump on its rim as shown. (a) Explain why the bump, from your viewpoint behind the car, executes simple harmonic motion. (b) If the radii of the car’s tires are 0.300 m, what is the bump’s period of oscillation? (c) What If? You hang a spring with spring constant k = 100 N/m from the rear view mirror of your car. What is the mass that needs to be hung from this spring to produce simple harmonic motion with the same period as the bump on the tire? (d) What would be the maximum speed of the hanging mass in your car if you initially pulled the mass down 8.00 cm beyond equilibrium before releasing it?
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