5) A mass on a spring is oscillating at a frequency of 17 Hz with a maximum disp

Question

5) A mass on a spring is oscillating at a frequency of 17 Hz with a maximum displacement of 6 cm. a) What is the period of oscillation? b) What is the maximum speed? c) What is the maximum acceleration? d) At what position or positions does the mass have the maximum acceleration? 6) Y(x,t) = Ae^ialphax e^-betat a) Show that the above function is a wave by showing that it satisfies the wave equation. A, alpha, beta are arbitrary constants, j is the imaginary constant equal to the square-root of negative one. b) Find the wave speed where alpha = 1, beta = 4 ,and A =3 7) A sinusoidal wave traveling in the +x direction has a wavelength of 20 cm, a period of 10 s, has a maximum displacement from equilibrium of 3 cm, and at x = 0 and t = 0. a) Write an equation describing this wave. b) What is the speed of the wave? c) What is the transverse speed of the wave at x = 0 when t = 5 s?

Explanation / Answer

given,

frequency = 17 Hz

displacement = 6 cm

time period = 1 / frequency

time period = 1 / 17

time period = 0.0588 sec

maximum speed = 2 * pi * frequency * A

maximum speed = 2 * pi * 17 * 0.06

maximum speed = 6.4088 m/s

maximum acceleration = (2 * pi * frequency)^2 * A

maximum acceleration = (2 * pi * 17)^2 * 0.06

maximum acceleration = 684.555 m/s^2

at maximum displacement or amplitude does the mass have maximum acceleration

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