一物体做简谐运动,振动方程为x=Acos(wt+1/2π),在t=0时刻的动能和t=T/8处的动能比一物体作简谐振动,振动方程为x=Acos(wt+π/2).则该物体在t=0 时刻的动能与t=T/8(T为振动周期)时刻的动能之比为
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![一物体做简谐运动,振动方程为x=Acos(wt+1/2π),在t=0时刻的动能和t=T/8处的动能比一物体作简谐振动,振动方程为x=Acos(wt+π/2).则该物体在t=0 时刻的动能与t=T/8(T为振动周期)时刻的动能之比为](/uploads/image/z/5571407-47-7.jpg?t=%E4%B8%80%E7%89%A9%E4%BD%93%E5%81%9A%E7%AE%80%E8%B0%90%E8%BF%90%E5%8A%A8%2C%E6%8C%AF%E5%8A%A8%E6%96%B9%E7%A8%8B%E4%B8%BAx%3DAcos%28wt%2B1%2F2%CF%80%29%2C%E5%9C%A8t%3D0%E6%97%B6%E5%88%BB%E7%9A%84%E5%8A%A8%E8%83%BD%E5%92%8Ct%3DT%2F8%E5%A4%84%E7%9A%84%E5%8A%A8%E8%83%BD%E6%AF%94%E4%B8%80%E7%89%A9%E4%BD%93%E4%BD%9C%E7%AE%80%E8%B0%90%E6%8C%AF%E5%8A%A8%2C%E6%8C%AF%E5%8A%A8%E6%96%B9%E7%A8%8B%E4%B8%BAx%3DAcos%EF%BC%88wt%2B%CF%80%2F2%EF%BC%89.%E5%88%99%E8%AF%A5%E7%89%A9%E4%BD%93%E5%9C%A8t%3D0+%E6%97%B6%E5%88%BB%E7%9A%84%E5%8A%A8%E8%83%BD%E4%B8%8Et%3DT%2F8%EF%BC%88T%E4%B8%BA%E6%8C%AF%E5%8A%A8%E5%91%A8%E6%9C%9F%EF%BC%89%E6%97%B6%E5%88%BB%E7%9A%84%E5%8A%A8%E8%83%BD%E4%B9%8B%E6%AF%94%E4%B8%BA)
一物体做简谐运动,振动方程为x=Acos(wt+1/2π),在t=0时刻的动能和t=T/8处的动能比一物体作简谐振动,振动方程为x=Acos(wt+π/2).则该物体在t=0 时刻的动能与t=T/8(T为振动周期)时刻的动能之比为
一物体做简谐运动,振动方程为x=Acos(wt+1/2π),在t=0时刻的动能和t=T/8处的动能比
一物体作简谐振动,振动方程为x=Acos(wt+π/2).则该物体在t=0 时刻的动能与t=T/8(T为振动周期)时刻的动能之比为多少?
一物体做简谐运动,振动方程为x=Acos(wt+1/2π),在t=0时刻的动能和t=T/8处的动能比一物体作简谐振动,振动方程为x=Acos(wt+π/2).则该物体在t=0 时刻的动能与t=T/8(T为振动周期)时刻的动能之比为
对x=Acos(wt+π/2)求t的导数,得速度v=ωAsinωt,ω=2π/T
t=0时v1=ωA,t=T/8时v2=ωA/√2
所以动能Ek1:Ek2=2:1
由振动方程x=Acos(wt+π/2)可知
t=0 时刻x=0质点在平衡位置速度最大
简谐振动机械能守恒 EP+EK=1/2KA^2
EK=1/2KA^2
t=T/8 W=2π/R x=Acos(wt+π/2)=2^1/2A
1/2KA^2=1/2KX^2+EK' EK'=1/4KA^2
EK/EK'=2:1
t=0时: x=Acos(ωt+π/2)=0 位移为零,所以速度最大,动能为:E1=1/2kA^2
t=T/8时:x=Acos(ω*T/8+π/2)= Acos(π/4+π/2)=-(2^1/2)/2 *A ,所以动能为:
E2=1/2k[(2^1/2)/2*A]^2
所以E1:E2=2:1