SHM Overview

SIMPLE HARMONIC MOTION

VOCABULARY

Oscillation (Oscillating Motion) - the back-and-forth motion of an object from an equilibrium position.

Restoring Force – a force which acts to bring a body to its equilibrium position. The restoring force is a function only of
position of the mass or particle, and it is always directed back toward the equilibrium position of the system.

Simple Pendulum – a dense mass (pendulum bob) on the end of a massless string. The maximum angle of displacement
for a simple pendulum should be less than 15 degrees.

Period (T) – The amount of time that a system takes for one complete oscillation. Period of a Pendulum: 𝑇𝑇=2𝜋𝜋√𝑙𝑙𝑔𝑔 Period
of a Mass-Spring: 𝑇𝑇=2𝜋𝜋√𝑚𝑚𝑘𝑘

Frequency (f) – the number of complete oscillations that are completed each second. Measured in Hertz (Hz) which is
the number per second. 𝑓𝑓=1𝑇𝑇

Equilibrium position - the resting position for a SHM system. The position in SHM where there is zero net force on the
mass.

Amplitude (A) – The maximum displacement from the equilibrium position of an object in simple harmonic motion.

VARIABLE RELATIONSHIPS- PENDULUM

•Every pendulum has a single period it oscillates at

•defined by ONLY the length of the string and the acceleration of
gravity

•Period of a pendulum increases as length increases (square root relationship)

•Period of a pendulum decreases as acceleration of gravity increases (inverse square
relationship)

EQUATION

• 𝑇 = 2𝜋
𝑙𝑙
𝑔𝑔

• T= Period

• 2𝜋= 6.28

Multiple Choice

What are the two missing variables for this pendulum oscillator?

• Mass (numerator) & spring (denominator)

• length (numerator) & gravity (denominator)

• mass (numerator) & gravity (denominator)

• length (numerator) & spring (denominator)

VARIABLE RELATIONSHIP- SPRING &
MASS

• Every mass-spring has a single period it oscillates at

• defined by ONLY the mass and the spring constant

• Period of a mass-spring increases as mass increases (square root
relationship)

• Ex. What would happen if the mass of the system was tripled?

• Increase by less than triple

• Period of a mass-spring decreases as spring constant increases (inverse
square relationship)

EQUATION

• 𝑇 = 2𝜋
𝑙𝑙
𝑔𝑔

• T= Period

• 2𝜋= 6.28

Multiple Choice

What are the two missing variables for this Spring- Mass oscillator?

• Mass (numerator) & spring (denominator)

• length (numerator) & gravity (denominator)

• mass (numerator) & gravity (denominator)

• length (numerator) & spring (denominator)

MOTION & FORCE

• Equilibrium Point is in the center of the oscillating
motion
•net force is zero at the equilibrium point
•equilibrium means balanced forces

• Restoring forces ALWAYS points toward the
equilibrium point

•

proportional to the displacement from the equilibrium point

SHM ENERGY

• SHM (without friction) is a classic example of conservation of energy

•for BOTH oscillating pendulum and mass-spring systems

• PEG at maximum at maximum displacement

• KE is maximum at equilibrium point

• Ex. An object is pulled from rest (x=0m) to reach x=5m. It oscillates
between x=5m and x=-5m. What is the max PE and max KE?

Multiple Choice

An object is pulled from rest (x=0m) to reach x=5m. It oscillates between x=5m and x=-5m. What is the max PE?

• X=5m

• X=5m & X=-5m

• X=0m

• X= -5m

Multiple Choice

An object is pulled from rest (x=0m) to reach x=5m. It oscillates between x=5m and x=-5m. What is the max KE?

• X=5m

• X=5m & X=-5m

• X=0m

• X= -5m