Oscillatory Motion

🎯 Class Objective:

The student applies Hooke’s law and energy relationships to solve oscillatory motion problems, analyzes experimental force–extension data, and evaluates the consistency between theoretical models and experimental results through graphical and analytical comparison.

🧲 A) Hooke’s Law (Spring)

1. A spring stretches 0.16 m when a force of 6 N is applied.
   Find k.
   
   

2. A spring has k=150 N/m.
   Find the force at x=0.12 m.

🔁 B) Energy in SHM

A mass–spring system has spring constant k = 150 N/m and amplitude A = 0.20 m.
Find the total mechanical energy using:

E = (1/2) k A²

If the amplitude is reduced to half its original value, the new energy becomes:

E/2 / E/4 / E/8

Explain your choice briefly.

🪀 C) Pendulum vs UCM (Mapping Activity)

Match each Simple Harmonic Motion concept to its corresponding Uniform Circular Motion idea:

• maximum displacement

• angular frequency

• equilibrium position

• restoring interaction

Choices (use each once):

• radius of the circle

• constant angular speed

• center of the circle

• inward force toward the center

🧩 D) Applied SHM Problem

A mass m = 0.80 kg oscillates on a spring with k = 50 N/m.

1. Find the angular frequency using:

ω = √(k/m)

2. If the amplitude is 0.12 m, find the maximum speed using:

vmax = ωA

3. If the amplitude increases, what happens to the maximum speed?
   Explain in one sentence.