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

March 6, 2022•171 words

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=A*d(cos(wt))/dt
v=-Awsin(wt) =A*(-sin(wt)),

a=dv/dt=d[(-Awsin(wt)]/dt=-Aw

*coswt*w

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=mw

^{2}

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]=-Aw

^{2}

SHM-graphs

img: