4.1

• $T=$$1/f$


  where

  T= period

  f= frequency
• oscillations: vibrations which repeat themselves


  velocity = 0 at the extreme

  velocity = max velocity at the middle
• a - peak/amplitude/crest

  b - wavelength

  c - trough

  
• at trough and amplitude, the velocity is 0.

  When velocity is at highest, it is at the equilibrium, where the acceleration is 0.
• the time period is the time it takes for the mass to make one full oscillation or cycle
• frequency (f) is measured in Hz (or cycles per second) and is defined as how many cycles of the wave occurs in a given time interval.
• one cycle of a wave is 2π. Half a cycle is π.
• energy in a simple harmonic system are just potential energy and kinetic energy. their sums are always constant but change at different parts of the motion. e.g., there is only potential energy at the amplitude of a pendulum and only kinetic energy at the equilibrium. however in between, there is a mix of both.
• in simple harmonic motion, at the equilibrium position, there is no net force

  in a pedulum, it is because the strings force of tension balances gravity

  in a spring, it is because the spring is uncompressed and puts no force on the mass.

  i.e., net force = mass x acceleration.

  acceleration = 0
• simple harmonic motion

  periodic motion around a point of central equilibrium where there is no net force but a restoring force that acts on the mass that is linearly proportional to the displacement from the equilibrium position and acts in an opposite direction from the displacement
• in a spring, it is hooks law:

  $F_s=$$-kΔx$

  where

  F=spring force

  k = spring constant

  x = displacement from equilibrium
• in a pendulum, it is gravity that provides the linear restoring force

  $y=$$mx+$$c$

  where

  y = restoring force

  m = gravity/ length of string

  x = displacement

  c=0