What is a damped simple harmonic motion? Explain clearly the effects of the damping force on the vibration of a body.

Explain how two simultaneous simple harmonic motions of a particle can produce motions along a straight line.

Explain how two simultaneous simple harmonic motions of a particle can produce motions along an ellipse

Explain how two simultaneous simple harmonic motions of a particle can produce motions along a circle.

A particle is executing S H M along a line $4 \mathrm{cm}$ Long. Its velocities when it crosses the middle point of its path is $12 \mathrm{cm} {\mathrm{s}}^{-1}$. Find the time period.

The amplitude of a particle executing SHM is $5 \mathrm{cm}$. When the particle is $2 \mathrm{cm}$ away from the mean position of its path, its acceleration is $8 \mathrm{cm} {\mathrm{s}}^{-2}$. What will be its velocity when it is $3 \mathrm{cm}$ away from the mean position? What is the force acting on the particle at that position, if its mass is $2 \mathrm{g}$.