APFIVE Period of a Massive Spring in Series
Two springs with spring constants $$k_1$$ and $$k_2$$ are connected in series. The first spring has a non-negligible mass $$m_1$$, while the second spring is ideal and massless. If a mass $$M$$ is attached to the free end, what is the period of oscillation?
A
$$T = 2\pi\sqrt{M(1/k_1 + 1/k_2)}$$
B
$$T = 2\pi \sqrt{\dfrac{M + m_1/3}{k_1 k_2/(k_1 + k_2)}}$$
C
$$T = 2\pi\sqrt{\dfrac{M}{k_1 k_2/(k_1 + k_2)}}$$
D
$$T = 2\pi\sqrt{(M + m_1)(1/k_1 + 1/k_2)}$$
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