Periodic and Oscillatory Motion - UNSOLVED PRACTICE SET

Q7. Define periodic motion. Give two examples from everyday life, one natural and one man-made.

Q8. What is the difference between periodic motion and oscillatory motion? Can all oscillatory motions be periodic? Explain with an example.

Q9. Define the following terms for oscillatory motion:

(i) Time period

(ii) Frequency

(iii) Amplitude

(iv) Angular frequency

Q10. A particle executes 20 oscillations in 5 seconds. Calculate its time period and frequency.

Q11. Explain why the motion of a planet around the Sun is periodic but not oscillatory.

Q12. The displacement of a particle is given by x = A cos(ωt + φ). Identify the physical quantities represented by A, ω, t, and φ.

Q13. Distinguish clearly between periodic motion and oscillatory motion with suitable examples. Explain why all oscillatory motions are periodic, but not all periodic motions are oscillatory. Give at least three examples of each type from nature and daily life.

Q14. A particle moves in a circular path of radius R with uniform angular speed ω. Show that the projection of this motion on any diameter executes simple harmonic motion. Derive the expression for:

(i) Displacement as a function of time

(ii) Velocity as a function of time

(iii) Acceleration as a function of time

Explain the physical significance of each result.

Q15. A student observes the following motions:

(i) The second hand of a clock

(ii) A child on a swing in the school playground

(iii) A car moving on a straight road at constant speed

(iv) A ball bouncing on the ground

For each motion, determine whether it is:

Periodic or non-periodic

Oscillatory or non-oscillatory

Justify your answers with clear reasoning.

Q16. A tuning fork vibrates at 440 Hz. The tip of one prong moves with an amplitude of 0.5 mm.

(i) Calculate the time period of oscillation.

(ii) Calculate the maximum speed of the prong tip.

(iii) Calculate the maximum acceleration of the prong tip.

(iv) Write the equation of motion for the prong tip, assuming it starts from the mean position.

Q17. A particle moves in a circle of radius 10 cm with a constant angular speed of 2 rad/s. The projection of this motion on the x-axis is observed.

(i) Write the equation of motion for the projected particle.

(ii) Calculate the time period of the projected motion.

(iii) Calculate the maximum speed and maximum acceleration of the projected particle.

(iv) At what positions does the projected particle have maximum speed? Maximum acceleration?

Q18. In a school science exhibition, a student sets up a demonstration where a small LED light is attached to the rim of a rotating bicycle wheel of radius 0.5 m. The wheel rotates at 2 revolutions per second. A screen is placed behind the wheel, and the shadow of the LED is observed.

(i) Describe the motion of the shadow on the screen.

(ii) Calculate the time period of the shadow's motion.

(iii) Calculate the amplitude of the shadow's motion.

(iv) Calculate the maximum speed of the shadow.

(v) Explain how this demonstration illustrates the connection between uniform circular motion and simple harmonic motion.