4. Water wheels are still used to power lumber mills in historic recreations. A typical water wheel makes one complete revolution every 90 seconds. A paddle starts its cycle 1m below the level of the water, and reaches a maximum height of 4m above the water. Assume that the timing starts when the paddle is at the top of the water wheel. a) What is the period of the water wheel? The amplitude? b) What is the radius of the water wheel? c) How high is the axle of the water wheel above the level of the water? d) What is the equation of the sinusoidal axis? e) Provide a table of values and a graph indicating 1 full cycle. Remember, your graph needs 5 critical values. f) What is the equation that represents this function?
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.
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