Physics

1. Physics

2. Session Simple Harmonic Motion - 2

3. Session Objectives

4. Session Objective Angular SHM Pendulum (Simple) Torsional Pendulum Horizontal Vibration of a spring Vertical Vibration of a spring Combination of springs in series Combination of springs in Parallel

5. Angular SHM

6. T x Simple Pendulum

7. Torsional Pendulum

8. Horizontal Vibrations of Spring Same result holds good for vertical vibrations of a spring also.

9. K2 K1 Keq Keq K1 K2 Springs – Series and Parallel

10. Questions

11. Find the spring constant for the spring system shown: (a) K3 K1 K1 K2 (b) K2 Illustrative Problem

12. Solution a) The two springs are in parallel so b) The springs are in parallel so

13. The spring constant for the adjoining combination of springs is • K b. 2K • c. 4K d. 2K K K Illustrative Problem

14. Class Test

15. The appropriate graph between time period T of angular SHM of a body and radius of gyration r is (a) (b) (c) (d) Class Exercise - 1

16. Solution Hence, answer is (a).

17. Which of the following graphs is appropriate for simple pendulum? (a) (b) (c) (d) Class Exercise - 2

18. So (a). and So (b). Solution All others are wrong except these. Hence, answer is (a) & (b).

19. Class Exercise - 3 A hollow metallic bob is filled with water and hung by a long thread. A small hole is drilled at the bottom through which water slowly flows out. The period of oscillations of sphere (a) decreases(b) increases(c) remains constant(d) first increases and then decreases

20. Solution As the water slowly flows out, the centre of gravity moves down. So the length increases and hence T increases. After half the sphere is empty, the centre of gravity begins to move up. So the length decreases and hence T decreases. Hence, answer is (d).

21. The total energy of a simple pendulum is E. When the displacement is half of amplitude, its kinetic energy will be (a) E (b) (c) (d) Class Exercise - 4

22. Now Solution Hence, answer is (b).

23. A spring has a spring constant K. It is cut into two equal lengths and the two cut pieces are connected in parallel. Then the spring constant of the parallel combination is(a) K(b)2K(c) 4K (d) Class Exercise - 5

24. Solution Spring constant of cut pieces K´ = 2K Now parallel combination of these results in a spring constant. = 4K Hence, answer is (c).

25. A spring of spring constant K is divided into nine equal parts. The new spring constant of each part is (a) 9K (b)(c) 3K (d) Class Exercise - 6

26. If force is constant, then Now let K´ be new spring constant. Then Solution We know that for springF = Kx or K´ = 9K Hence, answer is (a).

27. The amplitude of damped oscillator becomes one-half after t seconds.If the amplitude becomes after3tseconds, then n is equal to(a) (b) 8(c) (d) 4 Class Exercise - 7

28. Solution Hence, n = 8 Hence, answer is (a).

29. The angle f at which the mean position exists of a simple pendulum placed in acar accelerating by to right is (a) (b) (c) (d) None of these Class Exercise - 8

30. Solution T cosf = mg Hence, answer is (a).

31. Keg of following figure is (a) K1 + K2 + K3 + K4(b) (c)(d) None of these Class Exercise - 9

32. Solution When we displace the body from its mean position, we see the extension in all the springs is same. So the combination is parallel. Hence answer is (a).

33. What is the resultant time period of a particle, if following two SHMs in same direction when superimposed on each other is x1 = Asinwt, x2 = Acoswt? (a) (b) (c) (d) None of these Class Exercise - 10

34. So the time period = Solution X = X1 + X2 = A sinwt + A coswt Hence, answer is (a).

35. Thank you