1. Two mass-spring systems are experiencing damped harmonic motion, both at 1.2 cycles per second and both with an initial maximum displacement of 10 cm. The first has a damping constant of 0.8, and the second has a damping constant of 0.4. a. Find functions of the form to model the motion in each case. b. How do the two mass-spring systems differ? (Hint: Graph the two functions using Geogebra/any App or make a table of values for t and flt) to analyze its damnin g motion)
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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