Please, I need help with this HW, answer in details. The position of a mass osci
ID: 1454764 • Letter: P
Question
Please, I need help with this HW, answer in details.
The position of a mass oscillating on a spring is given by x = (1.6 cm) cos [2pi t/(2.78 s)]. What is the period of this motion? What is the first time the mass is at the position x = 0? The position of a mass oscillating on a spring is given by x = (8.0 cm) cos [2.7t/(0.75 s)]. What is the frequency of this motion? When is the mass first at the position x = -8.0 cm? Tuning forks are used in the diagnosis of nervous afflictions known as large-fiber polyneuropathies, which are often manifested in the form of reduced sensitivity to vibrations, diabetes and nerve damage from exposure to heavy metals. The tuning fork in the figure below has a frequency of 125 Hz. The tips of the fork move with an amplitude of 1.32 Disorders that can result in this type of pathology include mm. Find the maximum speed of the tips. Find the maximum acceleration of the tips. (Give your answer as a multiple of g.) A 0.58-kg mass attached to a spring undergoes simple harmonic motion with a period of 0.70 s. What is the force constant of the spring?Explanation / Answer
2.
Given
X=(1.6 cm)Cos[2pit/2.78s]
Compare it with
X=ACos(2pit/T)
TIme period
T=2.78 s
b)
Given X=0
=>0=(1.6 cm)Cos[2pit/2.78s]
2pit/2.78 =Cos-1(0) =pi/2
t=2.78/4
t=0.695 s =0.7 s(approx)
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3.
a)
Time period
T=0.75 s
frequency
f=1/T =1/0.75
f=1.33 Hz
b)
-8=8Cos[2pit/0.75s]
2pit/0.75 =Cos-1(-1) =pi
t=0.75/2 =0.375 s