Periodic Motion

All methods of production of musical sound depend upon the ability to produce periodic motion in some mechanical device which in turn produces sound. The important terms associated with periodic motion are frequency, period and amplitude. The frequency (f) is in cycles per second or Hertz and the period (T) is the number of seconds to complete one cycle or "seconds/cycle". The period, T, in seconds per cycle = 1/f. The amplitude is the maximum displacement away from the equilibrium position (the place where the object would normally rest). For example, the normal rest position of a violin string is its equilibrium position. The intensity produced by the string is related to the amplitude of its motion.

所有产生音乐声音的方法都依赖于能够使某种机械装置产生周期性运动的能力，而该装置进而产生声音。与周期性运动相关的术语有频率、周期和振幅。频率（f）是每秒的周期数或赫兹，周期（T）是完成一个周期所需的时间或“每周期秒数”。周期T（每周期秒数）=1/f。振幅是物体偏离平衡位置（物体通常静止的位置）的最大位移。例如，小提琴弦的正常静止位置就是其平衡位置。弦产生的强度与它的运动振幅有关。

One of the most common examples of periodic motion is the pendulum. Although it is not directly related to a sound source, it will serve to demonstrate some of the features of periodic motion. We will study the frequency of the pendulum as a function of the mass, length, and amplitude and plot graphs of the dependence upon these parameters.

周期性运动的一个最常见例子是单摆。尽管它与声音源没有直接关系，但它将用于展示周期性运动的一些特征。我们将研究单摆的频率作为质量、长度和振幅的函数，并绘制这些参数之间的依赖关系图。

1. Suspend the 200g mass provided to form a pendulum of length 150cm (measure from the center of mass to the point of support). Measure the time required to complete 10 full cycles to the nearest tenth of a second. Repeat for pendulum lengths of 100, 75, 50, and 25 cm. Calculate the period in seconds/cycle and the squares of the periods. Plot the period squared vs the length on the graph paper provided.

1. 将提供的200g质量悬挂起来，形成一个长度为150cm的单摆（从质心到支点的距离测量）。测量完成10个完整周期所需的时间，精确到十分之一秒。对长度为100cm、75cm、50cm和25cm的单摆重复上述测量。计算每个单摆的周期（秒/周期）以及周期的平方。将周期的平方与长度在提供的图纸上绘制图表。

长度总时间周期平方

150 厘米 __________ ________ ____________

100 厘米 __________ ________ ____________

75 厘米 __________ ________ ____________

50 厘米 __________ ________ ____________

25 厘米 __________ ________ ____________

2. Using successive masses 100, 200, and 500 grams, make a pendulum of length 50 cm and determine the corresponding periods. Since different masses cause different amounts of stretching of the string, the length should be adjusted to exactly 50 cm and remeasured for each mass. The length should be measured to the center of the hanging mass.

使用连续的100克、200克和500克质量，制作一个长度为50厘米的单摆，并确定相应的周期。由于不同的质量会使绳子产生不同的拉伸量，因此应将长度调整为恰好50厘米，并对每个质量重新测量。长度应测量到悬挂质量的中心。

质量 100 克 200 克 500 克

周期 __________ ________ ____________

将周期作为质量的函数绘制出来。

3. Using the 100 gm mass and a length of 50 cm, pull the pendulum bob out a distance of approximately 15 cm (straight line measure) and measure the period of the resulting motion when released. Repeat for 30, 45, and 60 cm. These distances may be measured by placing one end of the meter stick at the equilibrium point and measuring the straight line distance to the mass. Record the period.

3. 使用100克质量和50厘米的长度，将单摆球拉出约15厘米（直线测量），然后释放，测量由此产生的运动的周期。对30厘米、45厘米和60厘米重复此操作。这些距离可以通过将米尺的一端放在平衡位置，测量到质量的直线距离来测量。记录周期。

振幅：15 厘米 _______ 30 厘米 _______ 45 厘米 ________ 60 厘米 ________

4. Using the graph made in part 1, predict the period of a 125 cm pendulum. Measure the period and compare. What mass and amplitude should you use?

4. 使用第一部分制作的图，预测一个125厘米长的单摆的周期。测量实际周期并进行比较。应使用什么质量 and 振幅？

预测周期 ____________

测得的周期 ____________

5. How strongly does the period of a pendulum depend upon the mass of the bob and the amplitude of the swing?

5. 单摆的周期对摆球质量及摆幅的依赖程度如何？

6. If you had a pendulum type clock which was running too slow what could you do to correct it?

Introduction to Periodic Motion

Equipment: Periodic Motion