**Simple harmonic motion, damped oscillation, forced oscillation and resonance;**

Questions:

**Q 1.** During an earthquake, a horizontal shelf moves vertically. If its motion can be regarded as simple harmonic motion, calculate the maximum value of amplitude of oscillation so that the books resting on it stay in contact with it always. Take $g=9.9\ m/s^2$ and $T=0.5 s$ . **[10 marks]**

**Q 2. **What is Damped Harmonic Oscillation? Write the equation of motion and obtain the general solution for this oscillation. Discuss the cases of Deadbeat, Critical Damping and Oscillatory motion based on the general solution. What would be the logarithmic derement of the damped vibrating system, if it has an initial amplitude 30 cm, which reduces to 3cm after 20 complete oscillation? **[20 marks]
**

Video Solution at 11 pm