- #1
KMcFadden
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Homework Statement
Two pendula of length 1.00m are set in motion at the same time. One pendula has a bob of mass 0.050kg and the other has a mass of 0.100kg.
1. What is the ratio of the periods of oscillation?
2. What is the period of oscillation if the initial angular displacement is small?
3. What is the period of oscillation if the initial angular displacement is 60.0°? Calculate the series out to three terms.
Homework Equations
1. T=2π√(L/g)
2. T=2π√(L/g)[1+1^2/2^2 〖sin〗^2 (θ/2)+(1^2 3^2)/(2^2 4^2 ) 〖sin〗^4 (θ/2)+(1^2 3^2 5^2)/(2^2 4^2 6^2 ) 〖sin〗^6 (θ/2)]
The Attempt at a Solution
1. 1:2 or 2:1 depending on which you consider mass 1 or mass 2.
2. T=2π√(L/g)
T=2π√(1.00m/〖9.808m/s〗^2 )
T=2.01s
3. T=2π√(L/g)[1+1^2/2^2 〖sin〗^2 (θ/2)+(1^2 3^2)/(2^2 4^2 ) 〖sin〗^4 (θ/2)+(1^2 3^2 5^2)/(2^2 4^2 6^2 ) 〖sin〗^6 (θ/2)]
T=2π√(1.00m/〖9.808m/s〗^2 )[1+1^2/2^2 〖sin〗^2 (60/2)+(1^2 3^2)/(2^2 4^2 ) 〖sin〗^4 (60/2)+(1^2 3^2 5^2)/(2^2 4^2 6^2 ) 〖sin〗^6 (60/2)]
T=2.006[1+0.5000+0.0088+0.00153]
T=2.006[1.51033]
T=3.03s