1. A spring is mounted from the ceiling. As a mass is attached, the spring stret
ID: 2099515 • Letter: 1
Question
1. A spring is mounted from the ceiling. As a mass is attached, the spring stretches 0.73 m. The spring is then stretched an additional 0.4 m and released. What will be the frequency of the resulting oscillation? Your answer should be given to the nearest hundredth of a Hertz.
2. A 721-g mass vibrates according to the equation x=0.4 cos(3.6 t), where x is in meters and t is in seconds. What is the period of the oscillation? Your answer should be in seconds and given to the nearest hundredth of a second.
Explanation / Answer
1) mg = k(x1 + x2)
k/m = g/(x1 + x2)
m/k = (x1 + x2)/g
frequency of oscillation = (1/2pi) sqrt(m/k)
f = 0.533 Hz
f = 0.53Hz
b) x= 0.4 cos(3.6t)
w = 3.6
2*pi*f = 3.6
f = 5.654 Hz
period of oscillation = 1/f = 0.1768 sec
t = 0.18sec
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