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新教材在机械振动中讨论了单摆的周期,直接给出了单摆的周期公式:T=2π(1/g)~(1/2)(式中:T为单摆作简谐振动的周期;1为单摆的摆长;g为重力加速度),这是因为用初等数学无法完成单摆周期的求解。它应该是解微分方程求得的。 由于同学们对公式的来历不清楚,因此当单摆处于非常规情况下,求单摆的周期时就“无从下手”。笔者认为教学中可采用等效的方法处理该问题,以解决学生“无从下手”的困难。 首先,研究正常情况下单摆周期和g的关系。如图(1),设摆
The new textbook discusses the period of simple pendulum in mechanical vibration and gives the periodic formula of single pendulum directly: T = 2π (1 / g) ~ (1/2) (where T is the simple harmonic vibration 1 is the pendulum length and g is the gravitational acceleration), because the elementary mathematics can not solve the simple cycle. It should be solved by differential equations. Because students did not know the origin of the formula, so when the pendulum in unconventional circumstances, the cycle of seeking a single pendulum “impossible to start.” I believe that teaching can be used to deal with the equivalent method to solve the problem of “no beginning”. First, the relationship between the pendulum period and g under normal conditions is studied. Figure (1), set the pendulum