Ap physics u7

For any kind of motion to start there must be a net force

Net force, acceleration, velocity, and direction are all the same at the start

Shm

results when the magnitude of a restoring force (like centripetal force or Fnet) exerted on an object is proportional to the objects displacement from its equilibrium position (aka the acceleration is proportional to displacement from a fixed point and in the opposite direction).

spring restoring force eq (not rotating) (change in x / amplitude is ~x )

ma=-k*~x / Fnet=-k*~x

restoring position is also

equlibrium position

no motion means

Fnet=0

eq for torque in smh (rotating)

t=mgL*(theta) or t=-k*(theta)

k

mgL

the period of smh is related to

the frequency of the objects motion

pendulum period eq

T= 2pi * √(l/g) (l is length of string+ball)

spring period eq

T= 2pi * √(m/k)

equilibrium position is when

Fnet=0

smh only happens when motion is

periodic and has a restoring force

eq for period relative to disp

T= 4*(~x) → (4 max disps in one period)

position eq for shm (A=Amplitude)

-x= A*cos(2*pi*f*t) or -x= A*cos(w*t) or x= A*sin(2*pi*f*t)

w in shm

w is angular frequemcy and w=2*pi*f or w=2pi/T

max velocity eq in shm

v=A*w*cos(wt)

max acc eq in shm

v= -A*(w²)*sin(wt)

Period (T) and frequency (f) do not depend on

amplitude

period eq with w

T= 2pi/w

if a questions gives you the same diagram/formula in two different cases

that is a comparing question

in a graph question amplitde can be found by

finding the middle height and dividing by two (A= mid height/2)

total energy in shm

E= U+K (u → potential energy) (k → kinetic energy)

PE is zero in shm when (pendulum)

object is at center

PE is minimum in shm when

object is at center

PE is zero in shm when (spring)

object is at unstretched point, x=0, v=max, k=max

PE is max in shm when (spring)

a=max, Fs=max, v=min, k=min

PE eq for spring

U=(1/2)*k*(~x)²