Please i need help in this 4 questions!!!!! 1.A harmonic oscillator consisting o
ID: 1466813 • Letter: P
Question
Please i need help in this 4 questions!!!!!
1.A harmonic oscillator consisting of a spring with spring constant 11.5 N/m and an unknown mass has a frequency of 0.66 Hz. What is the mass?
2. A harmonic oscillator consisting of a spring with unknown spring constant and a mass of 0.49 kg has a period of 0.8 s. What is the spring constant (use units N/m)?
3. A harmonic oscillator that is used in an introductory physics lab consists of a spring with spring constant 38 N/m and a number of different masses that can get attached to the spring.
In the last week of the semester, the teaching assistant notices that all measured periods are about 22% higher than in the beginning of the semester. The TA suspects that the spring has been overstretched and that this has resulted in a permanent change of the spring constant. What is the new spring constant?
4. A simple harmonic oscillator consisting of a mass attached to a spring has a frequency of 2.62 Hz. If we now increase the mass by 24%, what is the new frequency of the oscillator?
Explanation / Answer
Formula f = (1/2pi) * sqrt(k/m)
k is spring constant
m is mass
sqrt(k/m) = 2pi f = 2* 3.14 * 0.66 = 0.07872
k/m = 0.0787^2 = 0.0062
m = 11.5/0.0062
m = 1885.24 kgs
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sqrt*(K/m) = 2pi/T = 2*3.14/0.8 = 7.85
K/m = 7.85^2 = 61.62
K = 61.62 * 0.49
K = 30.2 N/m
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use T is propo to sqrt(m/k)
T2/T1 = sqrt(k1/K2)
K2/K1 =(1/0.22)^2 = 20.66
K2 = 20.66 times k1
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f is inversy prop to sqrt(1/m)
f2/f1 = sqrt(m1/m2)
f2/f1 = sqrt(1/1.24)
f2 = 2.62 * 0.898
f2 = 2.35 Hz