6.1 AP Physics C: Mechanics

period for any SHM oscillator

T=\frac{1}{f}=\frac{2π}{ω}

period for a spring system

T=2π\sqrt{\frac{m}{k}}

period of a simple pendulum

T_p=2π\sqrt{\frac{L}{g}}

period of a physical pendulum

T_p=2π\sqrt{\frac{I}{mgh}}

frequency

f=\frac{1}{T}=\frac{ω}{2π}

displacement

x(t)=x_m*\cos{(ωt+φ)}

velocity

v(t)=-ω*x_m*\sin{(ωt+φ)}

acceleration

a(t)=-ω^2*x(t)

angular frequency for any SHM oscillator

ω=\frac{2π}{T}=2πf

angular frequency of a spring system

ω=\sqrt{\frac{k}{m}}

velocity amplitude

v_m=ωx_m

acceleration amplitude

a_m=ω^2x_m

spring force

F=-(mω^2)x=-kx

conservation of energy

E=U(t)+K(t)