**Short Questions**

1. A given spring is cut into two identical halves. Will the spring constant of each half increase, decrease or remain constant?

2. A simple pendulum set into vibration and left untouched eventually stop . Why?

3. A singer, holding a note of the right frequency ,can shatter a glass?

4. A wire hanges from a dark high tower so that its upper end is not visible. How can we determine the length of wire?

5. Briefly give two phenomena in which resonance plays an important role.

6. Calculate the length of simple pendulum of its frequency is 0.5 cps (g= 0 ms⁻²)?

7. Can we realize an ideal simple pendulum?

8. Can we realize an ideal simple pendulum?

9. Define angular displacement and write its S.I unit.

10. Define damping ?

11. Define driven harmonic oscillator and damped oscillations.

12. Define phase?

13. Define resonance. Give its examples?

14. Define restoring force and simple harmonic motion.

15. Define second pendulum? What id the length of second pendulum?

16. Define simple harmonic motion?

17. Define simple pendulum?

18. Define vibratory motion.

19. Describe free vibrations.

20. Describe some common phenomena in which resonance plays an important role.

21. Differentiate between damped oscillation and undamped oscillations.

22. Does frequency depend on amplitude for harmonic oscillator?

23. Does the acceleration of a simple harmonic oscillator remain constant during its motion? Is the acceleration ever zero? Explain?

24. Drive an experience for the time period of horizontal mass spring system?

25. Explain free and forced oscillations.

26. Explain the relation between total energy, potential energy and kinetic energy for a body oscillating with SHM?

27. Explain why in S,H,M. the acceleration is zero when the velocity is greatest?

28. Find the value of spring constant ?

29. Give examples of S.H.M?

30. Give one practical example of each of free and force oscillation ?

31. Give two applications in which resonance plays an important role?

32. How can you compare the masses of two bodies by observing their frequencies of oscillation when supported by a spring?

33. How cooking of food is possible in microwave oven?

34. How is a particular station tuned in the radio?

35. How the phenomenon of resonance is produced?

36. If a mass spring system is hung vertically and set into oscillations, why does the

37. If a mass spring system is hung vertically and set into oscillations, why does the motion eventually stop?

38. Is there a connection between F and X in mass spring system? Explain?

39. Name two characteristics of S.H.M.

40. Name two characteristics of simple harmonic motion?

41. Show that in SHM the acceleration is zero when the velocity is greatest and the velocity is zero when the acceleration is greatest?

42. Show that the acceleration of a body executing SHM is proportional to its displacement and is always directed towards its mean position?

43. State the basic conditions for frictionless system to execute simple harmonic motion?

44. Under what conditions does the addition of two S.H .Ms .produce a resultant, which is also simple harmonic?

45. What are damped oscillations? Give some of its applications.

46. What are damped oscillations?

47. What are free oscillation?

48. What do you mean by a driven harmonic oscillator?

49. What do you mean by phase?

50. What do you understand by forced vibrations? Explain with examples.

51. What happens to the frequency of a pendulum as its oscillator die down from large amplitude to small?

52. What happens to the period of simple pendulum if its length is doubled?

53. What is frequency of a second ,s pendulum ?

54. What is law of conservation of Energy in SHM?

55. What is mean by phase angle? Does it define angel between maximum displacement and the driving force?

56. What is meant by phase angle? Does it define angle between max displacement and the driving force?

57. What is meant by phase angle? Does it define angle between max displacement and the driving force?

58. What is restoring force?

59. What is the total distance travelled by an object moving with SHM in a time

60. What is the total distance travelled by an object moving with SHM in a time equal to its period, if its amplitude is A?

61. What is the wave from of SHM? Draw the curve?

62. What will be the frequency of simple pendulum if its length is 100cm?

63. Why are damping force often used on machinery?

64. Why soldiers are advised to break their steps when marching on a bridge?

65. Why the amplitude of lead bob is greater than pith ball as the bobs having equal size and length set into vibration?

66. Will the period of the vibrating spring increase, decrease or remain constant by addition of more weight?

67. Would you keep the amplitude of simple pendulum small or large. Why?

68. Write any three uses of simple pendulum?

**Long Questions**

1. Explain the relation between total energy, potential energy and kinetic energy for a body oscillating with SHM.

2. Describe some common phenomena in which resonance plays an important role?

3. State Hook‟s law. Write it in mathematical form.

4. Differentiate between free and forced oscillations.

5. Describe function of a microwave oven.

6. Which force actually provides the restoring force to the simple pendulum?

7. Define Simple Harmonic Motion (SHM). Show that motion of mass attached with a spring is SHM.

8. Define Simple Harmonic Motion (SHM). Derive the relation for instantaneous velocity for the projection of particle “P” moving in a circle.

9. Define Simple Harmonic Motion (SHM). Derive the relation for acceleration in terms of ω and displacement for the projection of particle “P” moving in a circle.

10. Define Simple Pendulum. Show that the motion of pendulum is SHM. Find relations for its time period and frequency.

11. Derive an expression for K.E and P.E of the mass spring system executing SHM. Also prove that its total energy remains conserved.

12. Write a note on Resonance

13. Discuss the motion of a horizontal mass spring system.

14. A 100g body hung on a spring, which elongates the spring by 4cm. When a certain object is hung on the spring and set vibrating, its period is 0.568s. What is the mass of the object pulling the spring?

15. A load of 15g elongates a spring by 2cm. If body of mass 294g is attached to the spring and is set into vibration with amplitude of 10cm, what will be its (i) period (ii) spring constant (iii) maximum speed of its vibration?

16. An 8 kg body executes SHM with amplitude 30cm. The restoring force is 60 N when the displacement is 30 cm. Find. (i) Period. (ii) Acceleration, speed, kinetic energy and potential energy when the displacement is 12cm.

17. A block of mass 4kg is dropped from a height of 0.8m on to a spring of spring constant k = 1960 N/m, Find the maximum distance through which the spring will be compressed.

18. A simple pendulum is 50cm long. What will be its frequency of vibration at a place where g = 9.8 ms⁻².

19. A block of mass 1.6kg is attached to a spring with spring constant 1000N/m, as shown is figure on book 7.14. The spring is compressed through a distance of 2cm and the block is released from rest. Calculate the velocity of the block as it passes through the equilibrium position, x = 0, if the surface is friction less.

20. A car of mass 1300kg is constructed using a frame supported by four springs. Each spring has a spring constant 20000N/m. If two people riding in the car have a combined mass of 160kg, find the frequency of vibration of the car, when it is driven over a pot hole in the road. Assume the weight is evenly distributed.

21. Find the amplitude, frequency and period of an object vibrating at the end of a spring, if the equation for its position, as a function of time, is: x= 0.25 cos((π/8)t) What is the displacement of the object after 2s?