Lisa's birthday is on October 18th. It's on Wednesday. She is going to have a birthday party. She wants to invite Peter, Gao Wei and Li Yan to her birthday party. They can celebrate after school. Today Lisa's parents go shopping with Lisa. They want to buy a My dream is to work in a hospital.I thin that a(n) __1__ is one of the most important jobs in the world.__2__ people are busy working every day 课时跟踪检测(三) 简谐运动的图像和公式
1．如图1(a)所示，一弹簧振子在AB间做简谐运动，O为平衡位置。图(b)是该振子做简谐运动时的x－t图像。则关于振子的加速度随时间的变化规律，下列图2四个图像中正确的是( )
图1
图2
2.一个质点做简谐运动的图像如图3所示，下列说法正确的是( )
图3
A．质点振动频率为4 Hz
B．在10 s内质点经过的路程为20 cm
3π
C．在5 s末，质点做简谐运动的相位为
2
D．t＝1.5 s和t′＝4.5 s两时刻质点的位移大小相等，都是2 cm
3．如图4甲所示，悬挂在竖直方向上的弹簧振子，周期T＝2 s，从最低点位置向上运动时开始计时，在一个周期内的振动图像如图乙所示。关于这个图像，下列说法正确的是
( )
Lisa's birthday is on October 18th. It's on Wednesday. She is going to have a birthday party. She wants to invite Peter, Gao Wei and Li Yan to her birthday party. They can celebrate after school. Today Lisa's parents go shopping with Lisa. They want to buy a My dream is to work in a hospital.I thin that a(n) __1__ is one of the most important jobs in the world.__2__ people are busy working every day 图4
A．t＝1.25 s时，振子的加速度为正，速度也为正B．t＝1.7 s时，振子的加速度为负，速度也为负
C．t＝1.0 s时，振子的速度为零，加速度为负向最大值D．t＝1.5 s时，振子的速度为零，加速度为负向最大值
4.如图5为某一质点的振动图像，由图可知，在t1和t2两时刻|x1|>|x2|，质点速度v1、
v2与加速度a1、a2的关系为( )
图5
A．v1
5．(北京高考)一个弹簧振子沿x轴做简谐运动，取平衡位置O为x轴坐标原点。从某时刻开始计时，经过四分之一周期，振子具有沿x轴正方向的最大加速度。能正确反映振子位
移x与时间t关系的图像是( )
图6
6.劲度系数为20 N/cm的弹簧振子，它的振动图像如图7所示，在图中A点对应的时刻
( )
图7
A．振子所受的弹力大小为0.5 N，方向指向x轴的负方向
B．振子的速度方向指向x轴的正方向C．在0～4 s内振子作了1.75次全振动
D．在0～4 s内振子通过的路程为0.35 cm，位移为0
7．如图8所示是某质点做简谐运动的振动图像，根据图像中的信息，回答下列问题：
Lisa's birthday is on October 18th. It's on Wednesday. She is going to have a birthday party. She wants to invite Peter, Gao Wei and Li Yan to her birthday party. They can celebrate after school. Today Lisa's parents go shopping with Lisa. They want to buy a My dream is to work in a hospital.I thin that a(n) __1__ is one of the most important jobs in the world.__2__ people are busy working every day
图8
(1)振幅、周期各是多大？
(2)写出这个简谐运动的位移随时间变化的关系式。
8．有一弹簧振子在水平方向上的B、C之间做简谐运动，已知B、C间的距离为20 cm，1
振子在2 s内完成了10次全振动。若从某时刻振子经过平衡位置时开始计时(t＝0)，经过
4
周期振子有负向最大位移。
(1)求振子的振幅和周期；
(2)画出该振子的位移－时间图像；
(3)写出振子的振动方程。
答 案
kx
1．选C 设弹簧劲度系数为k，位移与加速度方向相反，由牛顿第二定律得a＝－，
m故C正确。
1
2．选BD 由振动图像可直接得到周期为4 s，频率f＝＝0.25 Hz，故选项A是错误
T
高中物理课时跟踪检测三简谐运动的图像和公式教科版选修3_4
