Given / Data
HC Verma Chapter 12 Problem 7. Refer to your copy of Concepts of Physics Part 1 by H.C. Verma for the complete problem statement.
Concept / Formula
SHM restoring force F=-kx. x=A sin(omega*t+phi). omega=sqrt(k/m). T=2pi/omega. E=0.5kA^2=constant.
Step-by-step Solution
General approach for Chapter 12 Problem 7:
Step 1: Verify F proportional to -x.
Step 2: Find omega: sqrt(k/m) spring, sqrt(g/L) pendulum.
Step 3: Write x=A sin(omega t+phi); find A, phi from initial conditions.
Step 4: v=A omega cos(omega t+phi); max at x=0.
Step 5: Total energy E=0.5 k A^2=constant.
Key Equations
omega=sqrt(k/m) | T=2pi sqrt(m/k) | x=A sin(omega t) | v_max=A omega | a_max=A omega^2 | E=0.5 m omega^2 A^2
Final Answer
Apply the solution steps above. Cross-check with the HC Verma answer key for Chapter 12.
Common Mistakes
Assuming oscillation is SHM without verifying F proportional to -x; using wrong initial phase.
Quick Tip
Once omega is known: T=2pi/omega, v_max=A omega, a_max=A omega^2, E=0.5 m omega^2 A^2.
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