C1 Oscillations, Simple Harmonic Motion, Mass-spring system, Simple pendulum, SHM equatons

Oscillations
-Free oscillations occur when no external force is continously acting on a system
-Thus the energy of the system remains constant
-The system will oscillate at its natural frequency

{Simple Harmonic Motion
-Def - The oscillation of a system in which a force is continually trying to return the object to its equilibrium}
-This force(a.k.a restoring force) is directly proportional to the displacement from equilibrium position
Restoring force
F=-kx
F=resultant force a.k.a restoring force, x=displacement from equilibrium, k=proportionality constant dependent on the physical system
Period
-Period of SHM is the time taken to complete one oscillation
T=1/f
Mass-spring system
T=2pi2^{/m<--mass/k<--stiffness} constant
Simple Pendulum
T=2pi2^/l<--length of the string to the place attached to pendulum bob's centre of gravity/g<--gravitational
SHM equations
-An object undergoing simple harmonic motion oscillates sinusodally
graph img:
w=theta/t --> theta=wt, x=Acostheta; y=Asintheta, x=Acoswt, v=/\x//\t=dx/dt, v=d(Acos(wt))/dt=Ad(cos(wt))/dt
v=-Awsin(wt) =A(-sin(wt)),
a=dv/dt=d[(-Awsin(wt)]/dt=-Awcoswtw
a=-Aw^2cos(wt)
Simple Harmonic Motion
a=-Aw^2coswt, a=-w^2*Acos(wt), a=-w^2x, F=ma; F=-kx --> m(-w^2x)=-kx, w^2=k/m => k=mw²
w=2^/k/m
x=Acoswt, coswt=1, x[max]=A
v=-Awsinwt, max sinwt=1 v[max]=-Aw
min sinwt=-1, v[min]=Aw v[min]=Aw
a=-Aw^2coswt
a[max]=-Aw²
SHM-graphs
img: