A guitar string is pulled at point P a distance of 2 cm above its rest position. It is then released and vibrates in damped harmonic motion with a frequency of 155 cycles per second. After 1 s, it is observed that the amplitude of the vibration at point P is 0.7 cm. (a) Find the damping constant c. (Round your answer to two decimal places.) (b) Using the values given above, find an equation that describes the position of point P above its rest position as a function of time. Take t = 0 to be the instant that the string is released. (Use the rounded version of the damping constant you found above.)
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.
A guitar string is pulled at point P a distance of 2 cm above its rest position. It is then released and vibrates in damped harmonic motion with a frequency of 155 cycles per second. After 1 s, it is observed that the amplitude of the vibration at point P is 0.7 cm.
(a) Find the damping constant c. (Round your answer to two decimal places.)
(b) Using the values given above, find an equation that describes the position of point P above its rest position as a function of time. Take t = 0 to be the instant that the string is released. (Use the rounded version of the damping constant you found above.)
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