1. 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?

2. A parallel beam of light with a wavelength of $500nm$ passes through a narrow slit with a slit width of $2\mu m$. The angle of diffraction for the first minimum is θ. What is the new angle of diffraction for the first minimum when the slit width is changed to $4\mu m$ and the wavelength of the light is now $250nm$?

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. A beam of parallel light with a wavelength of λ is incident on a narrow slit. A diffraction pattern is formed on a distant screen. The angle of diffraction between the central maximum and the first minimum is θ. What would be the angle of the first diffraction minimum for the light with a wavelength of 3λ?

5. Light of wavelength λ1​ and λ2​ is incident on a diffraction grating with the slit spacing of $d$. A series of bright lines are formed on a screen.

What is the ratio sin θ1 /sin θ2 ​ ?

6. The graph shows the variation with time $t$ of the displacement $s$ of an object suspended by a spring. At what time is the acceleration in the negative direction at a maximum??

7. A monochromatic beam of light is incident on a double slit arrangement where the slit separation is 9.0×10^−5 m and the slit-screen distance is $1.0m$. The graph below shows the relative intensity of the light reaching the screen with respect to the distance from the central point of the pattern.

What is the wavelength of the light?

8. A train is traveling at 30ms^−1 towards a stationary observer. It sounds a horn of frequency $450Hz$.

Which of the following statements is true about the observed frequency compared with the emitted frequency as the train approaches?

9. 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?

10. A taut string on a guitar is fixed at both ends.

11. An object with a mass of $m$ is connected to a spring on a frictionless horizontal surface.

The object is displaced by $x$ from its equilibrium point O to point $A$ and executes simple harmonic motion with a period of $T$. Which of the following are true if the object is displaced by $2x$?

I. The angular frequency of the oscillation will be less.
II. Total energy of the object will be greater.
III. The average speed of the object will not change.

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

13. A string fixed at both ends oscillates in a standing wave as shown with a wavelength of $400mm$.

What is the length of the string?

14. 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.

15. 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?

16. A mass-spring system has a period of T0​. Another mass-spring system has a mass twice as large with a spring that requires four times as much force to obtain the same extension as the first system.

What is the new period in terms of T0​?

17. A wave is incident on a boundary between two media, $X$ and $Y$. The wave travels faster in medium $Y$ than in medium $X$

Which of the following diagrams shows a possible path for this wave?

A.				B.
C.				D.

18. A traveling wave is generated on a string tied to a speaker as shown.

Which of the following statements are correct about the travelling wave?

19. 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.

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.

22. An object executes simple harmonic motion with an amplitude of x0​. Which graph shows the relationship between the kinetic energy Ek​ and the displacement $x$ from the equilibrium position of the object?

A.			B.
C.			D.

23. 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.

24. 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.

25. 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?