Velocity and acceleration of SHM s+p)=eota+p+》 dx V= dt a 血=-02Acos(o1+p)=0.c0so1+9士π） 1、Vm=@4 velocity amplitude“速度幅”。 2、am=o2A acceleration amplitude m “加速度幅
) 2 sin( ) cos( A t v t dt dx v m cos( ) cos( ) 2 A t a t dt dv a m 1、 vm A velocity amplitude“速度幅 ”。 2、 acceleration amplitude “加速度幅 ”。 am A 2 Velocity and acceleration of SHM
Spring oscillator(弹簧振子) △△△个个M X By Hook's law F=- By Newton's second law of motion: d'x F=m dt" =kx
Spring oscillator（弹簧振子） F By Hook’s law F kx o x x By Newton’s second law of motion: k x dt d x F m 2 2
that is 0x=0 dt2 The solution: x=Acos(@t+o) Where A,and o are decided by the initial conditions
0 2 2 2 x dt d x that is x Acos(t ) x t m k Where A, and are decided by the initial conditions The solution:
Does the oscillator has same period when it free end hangs from the ceiling? Yo Equilibrium position mg
0 y free end Equilibrium position y o y mg F Does the oscillator has same period when it hangs from the ceiling?
The energy of SHM X X Kinetic energy: 女-mmsi) Potential E-3k-3k cos() energy: mo2 k
The energy of SHM sin ( ) 2 1 2 1 2 2 2 2 Ek m v m A t cos ( ) 2 1 2 1 2 2 2 Ep k x k A t m k 2 Kinetic energy: Potential energy: o x x v