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**PHYSICS TEST PAPER (OSCILLATIONS)**

**Time :**** 1 ½hr ****M. Marks: 40**

*Q.Nos**1 to 5 carries 1 mark each**QNos**6 to 10 carry 2 marks each**QNos**11 to 15 carry 3 marks each**QNos**16 – 17 carry 5 marks each*

1. What is periodic motion?

2. How will the time period of a simple pendulum change if its length is doubled?

3. Two identical springs of force constant k each are connected in series. What will be the equivalent spring constant?

4. What is the time period of a simple pendulum in a satellite orbiting around the earth? 5. What is the difference between forced oscillations and resonance?

6. Write expression for the particle velocity and acceleration during simple harmonic motion as function of time.

7. Derive expression for the instantaneous velocity and acceleration of a particle executing SHM.

8. What is an ideal simple pendulum? Write expression for its time period.

9. Show that the phase difference between displacement and acceleration is π/2.

10. Draw a graphical representation of SHM using displacement – time graph.

11. Show that the total energy in SHM is constant. Draw a graph showing the variation of KE, PE and Total Energy of SHM.

12. What are free oscillations and damped oscillations? Draw graphs to represent each.

13. Show that the horizontal oscillations of a mass less loaded spring are simple harmonic. Deduce expression for its time period.

14. A spring of force constant 1200 Nm^{-1} is mounted horizontally on a table. A mass of 3.0 kg is attached to the free end of the spring, pulled sideways to a distance of 2.0 cm and released. (i) What is the frequency of oscillation of the mass? (ii) What is the maximum acceleration of the mass? (iii) What is the maximum speed of the mass?

15. The acceleration due to gravity on the surface of moon is 1.7 ms^{-2}. What is the time period of a simple pendulum on the moon if its time period on earth is 3.5 s? Given g on earth = 9.8 ms^{-2}.

16. Define the terms harmonic oscillator, displacement, amplitude, cycle, time period, frequency, angular frequency, phase and epoch with reference to an oscillatory system.

17. Show that simple harmonic motion may be considered as the projection of uniform circular motion along the diameter of the circular path. Hence derive expression for the displacement of a particle in SHM.

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