pendulum VS spring

information
mass of block = mass of pendulum
spring constant = k
length of pendulm = l

free body diagram

* FBT = FBE
    ay = 0 m/s^2

comparison between two

simple harmonic

position

x(t) = A cos wt

y(t) = A sin wt

velocity

x(t) = -Aw sin wt
y(t) = wA cos wt

acceleration

x(t) = -w^2A cos wt
y(t) = -w^2A sin wt

this is position, velocity, and acceleration graphs

damped / critically damped / over-damped

damped

as a pendulum moves back and forth, friction exists which makes the speed of pendulum slow down

critically damped

The pendulum will stop as fast as possible at equilibrium which means pendulum does not go through equilibrium; for this, force applied to whole way down to equilibrium

over-damped

The pendulum very slowly stops at equilibrium; more force required than critically damped to whole way down to equilibrium

this is the case of damped in graph