Chapter 2: Periodic Motion

2.1 Equation of Simple Harmonic Motion (SHM)

2.2 Energy in SHM

2.3 Vertical Oscillation of Mass on a Spring

2.4 Angular SHM & Simple Pendulum

2.5 Oscillatory Motion (Damped, Forced & Resonance)

(a) Damped oscillation:

• Amplitude decreases gradually due to resistive force (air resistance, friction).
• Energy lost in each cycle.

(b) Forced oscillation:

• External periodic force applied to oscillator.
• Oscillator vibrates with frequency of driving force.

(c) Resonance:

• When driving frequency = natural frequency.
• Amplitude becomes maximum.
• Example: Breaking of glass by loud sound, soldiers not marching on bridge.

Important Questions and Answers in Short

Q1. Define SHM.
👉 Motion in which restoring force ∝ displacement and directed towards mean position.

Q2. Write equation of SHM.
👉 x = A sin(ωt + φ).

Q3. Write expressions for energy in SHM.
👉 K.E. = ½ mω²(A² − x²), P.E. = ½ mω²x², Total E = ½ mω²A².

Q4. Time period of vertical mass-spring system.
👉 T = 2π√(m/k).

Q5. Time period of simple pendulum.
👉 T = 2π√(l/g).

Q6. Define angular SHM.
👉 SHM where restoring torque ∝ angular displacement.

Q7. What is damping?
👉 Gradual decrease in amplitude due to resistive force.

Q8. Define forced oscillation.
👉 Oscillation under periodic external force.

Q9. Define resonance.
👉 Condition when driving frequency = natural frequency → maximum amplitude.

Q10. Give one example of resonance.
👉 Breaking of glass by sound of same frequency.

✅ Formula Sheet (Quick Revision):

• x = A sin(ωt + φ)
• ω = 2πf = √(k/m)
• T = 2π√(m/k) (spring), T = 2π√(l/g) (pendulum)
• K.E. = ½ mω²(A² − x²)
• P.E. = ½ mω²x²
• Total E = ½ mω²A²