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)