10. A block hangs on a spring attached to the ceiling and is pulled down 6 inches below its equilibrium position. After release, the block makes one complete up-and-down cycle in 2 seconds and follows simple harmonic motion. a. What is the period of the motion? b. What is the frequency? c. What is the amplitude?
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.
10. A block hangs on a spring attached to the ceiling and is pulled down 6 inches below its
equilibrium position. After release, the block makes one complete up-and-down cycle in 2
seconds and follows simple harmonic motion.
a. What is the period of the motion?
b. What is the frequency?
c. What is the amplitude?
d. Write a function to model the displacement ? (in inches) as a function of the time ? (in seconds) after release. Assume that a displacement above the equilibrium point is positive.
e. Find the displacement of the block and direction of movement at ? = 1 sec.
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