本题目来源于试卷: 2012美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
Inside a cart that is accelerating hori 3v3hmabf-emu2ks1n o0m n d 97zontally at acceleratio ewehrxe2xp(-6f .z+zrs4m8 . jy- qryn $\vec{a}$, there is a block of mass $M$ connected to two light springs of force constants $k_{1}$ and $k_{2}$. The block can move without friction horizontally. Find the vibration frequency of the block. 
A. $\frac{1}{2\pi}\sqrt{\frac{k_{1}+k_{2}}{M}+a}$
B. $\frac{1}{2\pi}\sqrt{\frac{k_{1}k_{2}}{(k_{1}+k_{2})M}}$
C. $\frac{1}{2\pi}\sqrt{\frac{k_{1}k_{2}}{(k_{1}+k_{2})M}+a}$
D. $\frac{1}{2\pi}\sqrt{\frac{|k_{1}-k_{2}|}{M}}$
E. $\frac{1}{2\pi}\sqrt{\frac{k_{1}+k_{2}}{M}}$
参考答案: E
本题详细解析:
The constant horizontal accelera+nt8 d(dz47v br6nnhttion $\vec{a}$ of the cart acts as a non-inertial frame. This introduces a constant pseudo-force $F_{pseudo} = -M\vec{a}$ on the block. A constant force only shifts the equilibrium position of the oscillation. It does not change the restoring force or the period/frequency of oscillation.
The two springs are in parallel, as a displacement $x$ stretches one and compresses the other, both creating a restoring force in the same direction.
The effective spring constant is $k_{eff} = k_1 + k_2$.
The frequency $f$ of a mass-spring system is $f = \frac{1}{2\pi}\sqrt{\frac{k_{eff}}{M}}$.
$f = \frac{1}{2\pi}\sqrt{\frac{k_{1}+k_{2}}{M}}$.
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