※ 引述《nerv3890 (阿渊)》之铭言： : [领域] (题目相关领域) : 简谐 : [来源] (课本习题、考古题、参考书...) : 考古 : [题目] : 3.A pendulum of length L and mass M has a spring of force constant k : connected to it at a distance h below its point of suspension as shown in a : figure below. Find the period of vibration of the system if the amplitude of : vibration is small. Assume the vertical suspension of length L is rigid and : its mass is negligible. : _____________________ : | | : |h | : | | : L |__ /\ ____| : | \/ \/ | : | k | : O : M : [瓶颈] (写写自己的想法，方便大家为你解答) : 初步构想 : 是设力矩τ=-CΘ : Θ为摆动角度，C为常数 : 之後就都没想法了...Orz : 有人能帮解答吗 : 感恩 如下图所示..以悬挂点作为支点..设系统角加速度为α..顺时针为正.. http://www.wretch.cc/album/show.php?i=kramnik1&b=34&f=1825180178&p=11 因为"Assume the vertical suspension of length L is rigid".. 根据力矩守恒 M*g*sinθ*L + F(spring)*cosθ*h = -M*L^2*α ..............(a) 因为"the force constant of spring is k" F(spring) =k*h*sinθ .....................................(b) 由(a)(b)知 M*g*sinθ*L + k*h^2*sinθ*cosθ = -M*L^2*α ..............(c) 因为"the amplitude of vibration is small" 对(c)做θ泰勒展开1阶近似..可得 M*g*L*θ + k*h^2*θ = -M*L^2*α θ = -M*L^2/(M*g*L + k*h^2)*α.............................(d) (d)式之解为 θ = A^(i*w*t) ,其中 w = M*L^2/(M*g*L + k*h^2) 设The period of vibration of the system为T..则 T = 2*π/w = 2*π*(M*g*L + k*h^2)/(m*L^2) --

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