Please show work so that I can compare my work and answers. Thanks! 1) A 0.51-kg
ID: 1467187 • Letter: P
Question
Please show work so that I can compare my work and answers. Thanks!
1) A 0.51-kg mass is hanging from a spring with spring constant 13 N/m. Then the mass is displaced from the equilibrium by 2.1 cm and let go. What is the resulting angular frequency of the oscillation?
(use rad/s as units)
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2) 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.
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?
Explanation / Answer
here,
mass , m = 0.51 kg
spring constant , k = 13 N/m
the angular frequency , w = sqrt( k/m)
w = sqrt( 13/0.51)
w = 5.05 rad/s
the angular frequency is 5.05 rad/s
2)
let the new spring consatnt be k2
k1 = 38 N/m
time period for 1 ,
T1 = 2*pi*sqrt(m/k1)
then time period for T2
T2 = T * (1 + 0.22)
2*pi*sqrt(m/k2) = 1.22* 2*pi*sqrt( m/k1)
1/k2 = 1.22^2/k1
k2 = 38/1.22^2
K2 = 25.53 N/m
the new spring constant is 25.53 N/m