机械振动模型

题目

在粗糙水平面上的一个弹簧振子，物体质量为$m$，弹簧的劲度系数为$k$，物体和水平表面之间的动摩擦因素为$\mu$，起始时物体的位置坐标为$x=A$，且速度为0，问：物体会停止在弹簧没有伸缩的地点吗？物体能振动多少次？

程序演示

程序源码

from vpython import *
m=0.5
k=10
dt=0.001
t=0
u=0.05
g=9.8
spring_length=1.5
scene=canvas(width=300,height=300,background=vec(0.5,0.6,0.5))
floor=box(pos=vec(0,0,0),length=3,height=0.01,width=1)
wall=box(pos=vec(-1.5,0.25-0.005,0),length=0.01,height=0.5,width=1)
square=box(pos=vec(0.5,0.1,0),length=0.2,height=0.2,width=0.2,texture=textures.wood,v=vec(0,0,0))
spring=helix(pos=vec(-1.5,0.1,0),radius=0.06,coils=15,thickness=0.03)
spring.axis=square.pos-spring.pos
figure=graph(width=300,height=300)
xtfigure=gcurve(graph=figure,color=color.red)

while t<5000:
    rate(1000)
    a=-(k*(spring.length-spring_length)/m)*spring.axis.norm()-u*g*square.v.norm()
    square.v=square.v+a*dt 
    square.pos=square.pos+square.v*dt
    spring.axis=square.pos-spring.pos
    xtfigure.plot(t,square.v.x)
    t=t+dt