Physics Worksheet

📈 Simple Harmonic Motion

Chapter: Mechanics · Level ★★☆ · Time: 30 min

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After this worksheet you can

Understand: Defining Condition for SHMUnderstand: Mass on a SpringUnderstand: Simple Pendulum (Small Angles)Understand: Position, Velocity, and Acceleration in SHM

📚 Quick Recap

Simple harmonic motion (SHM) is the most fundamental type of oscillation, where the restoring force is directly proportional to displacement — producing smooth, predictable sine-wave motion.

🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4

1A 4 kg mass on a spring with k=16 N/m. Find the period.

2Find the period of a pendulum with length 2.45m (g=9.8).

3A spring's period is measured at 4s with a 2kg mass. Find its spring constant k.

4Why does the period of a simple pendulum NOT depend on its mass?

🧮 Section B · Problem Solving ● INTERMEDIATE 4 × 3 = 12

5Why does the period of a mass-spring system depend on mass, but a pendulum's period does not?

6At what point in SHM is potential energy at its maximum?

7If a pendulum's length is quadrupled, how does its period change?

8If a spring's spring constant k is quadrupled (mass unchanged), how does the period change?

🚀 Section C · Challenge ● CHALLENGE 2 × 2 = 4

9What shape does a graph of position vs. time take for an object in SHM?

10Why is SHM considered the most 'fundamental' type of oscillation in physics?

💭 Reflection — the most useful thing I learned:

A ___/4 B ___/12 C ___/4 Total ___/20 Teacher's Signature Parent's Signature

✂ answer key — fold or cut before handing out

1 = T=2*pi*sqrt(4/16)=2*pi*0.5=pi≈3.14s 2 = T=2*pi*sqrt(2.45/9.8)=2*pi*0.5=pi≈3.14s 3 = 4=2*pi*sqrt(2/k), solve: sqrt(2/k)=4/(2pi)≈0.637, 2/k≈0.405, k≈4.94 N/m 4 = Mass cancels out of the pendulum equation T=2*pi*sqrt(L/g), leaving only length and gravity as factors | 5 = In a spring system, inertia (mass) directly resists the spring's restoring force, while a pendulum's restoring force is gravity acting on the same mass that provides the inertia, causing mass to cancel out 6 = At the maximum displacement (the extremes of motion) 7 = It doubles, since period is proportional to the square root of length 8 = It is halved, since period is inversely proportional to the square root of k | 9 = A sine or cosine wave 10 = Its simple proportional relationship between force and displacement makes it mathematically tractable and it appears as an approximation in many real physical systems