Answer to Question #206849 in Classical Mechanics for Rae

Question #206849

The period of a mass-on-spring oscillator is 3 seconds. Upon decreasing its mass by 500 g, the period will become 2 seconds.

a) Calculate the original mass!

b) Calculate the spring constant! 


Could you please explain in detail how to use the equation below?

T=2πm/kT=2\pi√m/k


1
Expert's answer
2021-06-14T17:26:43-0400

a)

T=2πmk,    T=2\pi \sqrt{\frac{m}{k}},\implies k=4π2mT2,k=\frac{4\pi^2m}{T^2},

T1=2πmm1k,    T_1=2\pi \sqrt{\frac{m-m_1}{k}},\implies

m=m1T2T2T12=0.5994=0.9 kg,m=\frac{m_1T^2}{T^2-T_1^2}=\frac{0.5\cdot 9}{9-4}=0.9~kg,

b)

k=43.1420.99=3.95 Nkg.k=\frac{4\cdot 3.14^2\cdot 0.9}{9}=3.95~\frac{N}{kg}.


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