Chapter 12 Oscillations The solution of this derivation equation is ACos(ot+l Oscillation Equation 积分常数,根据初始条件确定 Feature of Oscillatory Motion Dynamics: f=-k or a=-Ofx Kinematics: Motion function is sine or cosine form
Chapter 12 Oscillations The solution of this derivation equation is: —— Oscillation Equation Feature of Oscillatory Motion: Dynamics: f kx or a x 2 = − = − Kinematics: Motion function is sine or cosine form. 积分常数，根据初始条件确定 x = Acos(t +)
Chapter 12 Oscillations Problemll on page 317 from the springs so we hay 油tk+t We find the frequency of vibration from m2:0+a
Chapter 12 Oscillations Problem11 on page 317
Chapter 12 Oscillations ProblemI7 on page 318 17. We use a coordinate system with down positive. With xo positive, at the equilibrium position we have ∑F=-k0+mg=0 If the spring is compressed a distance x(so x is negative)from the equilibrium position, we have ∑F=-(x+x)+mg When we use the equilibrium condition, we get x0 ∑F=F=-kx x=0 Note that r is negative, so the restoring force is positive(down) If we stretch the spring a distance x(so x is positive), we still have ∑F==Kx+x)+mg When we use the equilibrium condition we get ∑F=F=-kx Note that x is positive, so the restoring force is negative(up)
Chapter 12 Oscillations Problem17 on page 318
Chapter 12 Oscillations 2 Basic Quantities of SHM: (P301) Displacemnt at time t Where xm(A),a, Phase and are x(1)= Im cOS(Ot+φ) constants. They are basic Amplitude Ime characteristic Angular Phase quantities of a frequency constant SHM(描述简谐振 or phase angle 动的特征量)
Chapter 12 Oscillations 2 Basic Quantities of SHM: (P301) Where xm (A), , and are constants. They are basic characteristic quantities of a SHM (描述简谐振 动的特征量)
Chapter 12 Oscillations Amplitude(振幅) xor A(4>0):2p298 (1)xm is called the amplitude (R PE)of the motion, it is a positive constant because the amplitude is the magnitude of the maximum displacement of the particle in either direction 表示质点可能离开原点的最大位移。A=xm 由初始条件决定,表征了系统的能量。(4恒>0) xx-t图
Chapter 12 Oscillations i. Amplitude (振幅) xm or A (A > 0): p298 (1) xm is called the amplitude（振幅） of the motion, it is a positive constant because the amplitude is the magnitude of the maximum displacement of the particle in either direction. 表示质点可能离开原点的最大位移。 由初始条件决定，表征了系统的能量。(A恒0) max A = x x −t 图 A − A x T 2 T t o