A guitar string vibrates at a frequency of 440 Hz. A point at its center moves i

Question

A guitar string vibrates at a frequency of 440 Hz. A point at its center moves in SHM with an amplitude of 3.0 mm and a phase angle of zero

A. Write an equation for the position of the center of the string as a function of time.

B. What is the maximum value of the magnitude of the velocity of the center of the string?

C. What is the maximum value of the magnitude of the acceleration of the center of the string

D. The derivative of the acceleration with respect to time is a quantity called the jerk. Write an equation for the jerk of the center of the string as a function of time.

E. Find the maximum value of the magnitude of the jerk.

Explanation / Answer

given

A guitar string vibrates at a frequency of 440 Hz. A point at its center moves in SHM with an amplitude of 3.0 mm and a phase angle of zero

1.
x 0.0030cos(2800t) m
2.
|v| 8.3 m/s
3.
|a| 23,000 m/s^2
4.
j 64,000,000sin(2800t) m/s^3
5.
|j| 64,000,000 m/s^3

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