Oscillatory Motion

🎯 Class Objective:

The student connects oscillatory motion to uniform circular motion by mapping correspondences between variables, applies Hooke’s law and basic energy relationships, and creates analogies between spring–mass and pendulum systems to explain simple harmonic motion.

🧲 A) Hooke’s Law (Spring)

1. A spring stretches 0.08 m when a force of 12 N is applied.
   Find k.
   
   

2. A spring has k=250 N/m.
   Find the force at x=0.06 m.

🔁 C) Energy in SHM

1. A mass–spring system has k=200 N/m and amplitude A=0.10 m.
   Find total mechanical energy E=(1/2) k A^2.
   
   

2. If amplitude doubles, energy becomes:
   
   

• 2E / 4E / 8E

🪀 D) Pendulum vs UCM (Mapping Activity)

Match the Simple Harmonic Motion concept to a Uniform Circular Motion idea:

• amplitude  A
  
  

• angular frequency ω
  
  

• equilibrium position
  
  

• restoring force
  
  

Choices (use each once):

• radius r
  
  

• constant angular speed
  
  

• center point
  
  

• inward net force
  
  

🧩 E) ICFES-Style Problem

A mass m=0.50 kg oscillates on a spring with k=80 N/m.

1. Find angular frequency ω^2 = k/m​.
   
   

2. If amplitude is 0.15 m, find max speed vmax​ = ω A .