1. An object on a horizontal spring performs simple harmonic motion. The position of the object as a function of time is given by x=5 cos⁡(2t).

Which of the following expressions gives the acceleration of this object as a function of time?

2. The graph below shows the variation with displacement $x$ of the acceleration $a$ from the equilibrium position of a particle that undergoes simple harmonic motion.

The magnitude of the slope of the graph is directly proportional to

3. A spring-mass system executes simple harmonic motion with an amplitude of $20cm$ and maximum elastic potential energy of $100J$. What is the displacement of the mass when the elastic potential energy of the system is $25J$?

4. Sound waves in water travel approximately 4.5 times faster than in air. Which of the following diagrams correctly shows the wavefronts of sound as they pass from air to water?

A.				B.
C.				D.

5. A mass $M$ hangs in equilibrium on a spring. The mass is pulled down 10$cm$ below the equilibrium position and released. It oscillates vertically about the equilibrium position performing simple harmonic motion.

If it takes 0.5 $s$ after release to return to its equilibrium position, which of the following is true for its first oscillation?

6. Water drips onto a pond every 3.0 seconds. The speed of water waves in the pond has been measured to be 1.2ms^−1. What is the wavelength of water waves generated because of the drops?

7. Two identical objects $P$ and $Q$ are connected to identical springs. Both $P$ and $Q$ are performing simple harmonic motion (SHM) around equilibrium level $O$.

The diagram shows positions of $P$ and $Q$ at time $t=0$. Which graph shows how kinetic energy of $P$ and $Q$ vary with time $t$?

A.				B.
C.				D.

8. A student carried out an experiment using a laser beam incident on double slits with negligible widths. An interference pattern is observed on a distant screen.

Which of the following is correct for the pattern observed on the screen when the slits of non-negligible widths are used with the same slit separation?

I. It is modulated with the single slit diffraction effect
II. Central maximum is brighter
III. Fringe spacing is larger

9. A $50cm$ string that is fixed at both ends produces a standing wave in the third harmonic. The speed of the wave on the string is 200 ms^−1

What is the frequency of oscillation?

10. A thin beam of monochromatic blue light is incident upon a single slit barrier. The emerging light then passes through a double slit arrangement and falls on a screen some distance away.

An interference pattern is observed on the screen. In order to increase the distance between adjacent fringes, which of the following actions would be appropriate?

11. A radio with a bright light is placed outside the doorway of long, dark room as shown. A student in a corner near the door can hear the sound of the radio while standing in the dark region of the room.

Which property of waves correctly explains why light does not reach her while the sound does?

12. The bob on a conical pendulum is rotated at constant speed such that it describes a horizontal circle of diameter 15$cm$. A lamp is placed so that the shadow of the bob projected on a screen describes simple harmonic motion. What is the displacement of the shadow after the bob has traveled a total distance of 30$\pi$ cm?

13. For a body executing simple harmonic motion, which statement is not possible?

14. In a single slit diffraction experiment, incident light passes through an aperture and a diffraction pattern is observed on a distant screen. $X$ is a point on the screen between the second-order minimum and the first-order minimum. $Y$ is a point at the centre of the principal maximum.

Which one of the following could be the ratio of the intensity of light on X to the intensity of light on $Y$?

15. A body performs simple harmonic motion (shm). Which of the following could be the speed against the time graph for one period of motion?

A.				B.
C.				D.

16. A simple pendulum undergoes simple harmonic motion. The graph shows the variation of a quantity $y$ with horizontal displacement x from the equilibrium position.

Which of the following quantities could be represented by quantity y?

17. Two simple pendulums with lengths $16L$ and $9L$ have masses $4M$ and $3M$ respectively. The period of the mass of $M$ is T. What is the period of mass of $3M$?

18. A boy tied two identical ropes to a fixed wall for a fitness exercise. He shakes the ropes to form waves.

A point on the right rope oscillates with a period of $0.4s$. A point on the left rope oscillates with a period of $0.2s$.

What is the ratio = wavelength of right rope/wavelength of left ?

19. A laser beam passes through a narrow slit and incident on a screen. A diffraction pattern is observed on the screen. The variation of intensity $I$ of light on the screen with distance $x$ is seen in the graph below.

Which of the following graphs best represents intensity distribution with distance when the slit is replaced by one of greater width? The original distribution is shown with a dashed line.

A.				B.
C.				D.

20. The diagram shows a beam of light passing from medium $X$ to medium $Y$.

If the angle of incidence of the light increases, which of the following changes can be implemented to keep the angle of refraction the same?

I. Medium X can be replaced with another medium which has a lower refractive index.
II. Medium X can be replaced with another medium which has a higher refractive index.
III. Medium Y can be replaced with another medium which has a higher refractive index.

21. Wavefronts travel across a boundary between two media as shown.

Which of the following correctly describes the change, if any, in the speed, wavelength and frequency of the waves as they pass from across the boundary?

22. A light ray is incident on a semicircular glass block from the air. The glass has a greater refractive index than air. Which diagram correctly represents a possible path of the light ray as it enters and leaves the block?

A.				B.
C.				D.

23. A traveling source produces sound waves nearby a child. The wavefronts of the sound waves and the position of a child are seen in the figure below.

The frequency of the generated sound waves is $f$. Which of the following is correct for both the direction of motion of the source and the observed frequency of the sound waves by the child?

24. A parallel beam of light passes through two parallel slits and an interference pattern is formed on a distant screen. The fringe separation is too small to measure. Which of the following would increase the fringe separation?

I. Increase the distance between slits and screen
II. Replace the light source with one with a longer wavelength
III. Increase the slit separation

25. A particle undergoes simple harmonic motion. Which of the following can be an expression of acceleration $a$ in terms of displacement $x$ and a constant value $k$?