308 million people live on the planet Trigonometry. One day, as an experiment, all 308 million people climbed on tables and jump off (t=0) at the same time. The shock wave as they hit the surface starts the entire Trigonometry planet vibrating in such a way that its surface first moves down from its normal position, and then moves up an equal distance above its normal position. The lowest point the ground reached was 50 feet below the normal position, which occurred at t= 13.5 minutes. Assume the displacement of the surface was a sinusoidal function of time. A. What is the amplitude of the vibration? Use a complete sentence to explain what the amplitude is and what it represents in the context of this scenario. B. What is the period of the vibration? Use complete sentences to explain how you determined the period of the vibration and what it represents in the context of this scenario. C. Sketch the graph showing displacement versus time. Label all axes and clearly represent important features of the graph. D. Write an equation expressing displacement in terms of time elapsed. Show all work and provide explanations for each calculation as it relates to the parent function. E. When would the ground's displacement be +15 feet for the 2nd time? F. Over the first hour and 48 minutes, find the time intervals when the ground's distance from its normal position is increasing. Use complete sentences to explain how you determined the intervals.
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.
308 million people live on the planet Trigonometry. One day, as an experiment, all 308 million people climbed on tables and jump off (t=0) at the same time. The shock wave as they hit the surface starts the entire Trigonometry planet vibrating in such a way that its surface first moves down from its normal position, and then moves up an equal distance above its normal position. The lowest point the ground reached was 50 feet below the normal position, which occurred at t= 13.5 minutes. Assume the displacement of the surface was a sinusoidal function of time.
A. What is the amplitude of the vibration? Use a complete sentence to explain what the amplitude is and what it represents in the context of this scenario.
B. What is the period of the vibration? Use complete sentences to explain how you determined the period of the vibration and what it represents in the context of this scenario.
C. Sketch the graph showing displacement versus time. Label all axes and clearly represent important features of the graph.
D. Write an equation expressing displacement in terms of time elapsed. Show all work and provide explanations for each calculation as it relates to the parent function.
E. When would the ground's displacement be +15 feet for the 2nd time?
F. Over the first hour and 48 minutes, find the time intervals when the ground's distance from its normal position is increasing. Use complete sentences to explain how you determined the intervals.
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