Important questions of oscillations-

1. What is meant by periodic and oscillatory motion? Distinguish between them.

2. What is meant by SHM . Find the expressions for displacement , velocity and acceleration. Also find the phase difference between them.

3. Find the potential energy and kinetic energy of a SHM and hence show that total energy is conserved . In what position of the oscillation is the energy wholly kinetic and wholly potential?

4. Prove that for an harmonic motion time period T = 1/2π(spring factor/inertial factor)^{1/2}.

5. What is simple pendulum? Derive expression for the time period or frequency of the oscillating simple pendulum. Also explain the second pendulum and find the length of the second pendulum on the surface of earth.

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6. Show that vibration of the liquid in the U-Tube is simple harmonic and also find the expression for the time period and frequency .

7. Explain the term (i) Free vibration (ii) Forced vibration (c) Resonant vibration (d) Damped oscillation.

8. A cylinder floating in water is temporarily pushed down . Derive an expression for its frequency.

9. Obtain an expression for the time period of a loaded and massless spring (i) Oscillating horizontally (ii) oscillating vertically . Show that is the same as the simple pendulum of length equal to the extension of the spring?

Numericals-

1. A body describe S.H.M. with am amplitude of 5cm . and a period of 0.2sec . Find the acceleration and velocity of the body when the displacement is (a) 5cm (b)3cm (c)0cm.

2. Simple pendulum of length l and having a bob of mass m is suspended in a car . The car is moving on a circular path of radius R with a uniform speed v . If the pendulum makes small oscillation in a redial direction about its equilibrium position . What will be its time period?

3. A spring balance has a scale that reads from 0 to 50 kg . the length of the scale is 20cm. A body suspended from this balance when displaced and released , oscillation with a period of 0.60 sec. What is the weight of the body? Ans-219N

4. The acceleration due to gravity on the surface of the moon is 1.7m/s^{2}. What is the time period of the simple pendulum on the moon if its time period on the surface of the earth is 3.5sec? Ans-8.4 sec

5. A spring with spring constant 1200N /m is mounted on the horizontal frictionless table , a mass of three kg it attached to the free end of the spring . The mass is then pulled sideway to a distance of 2cm and released . Determine (a) the frequency of oscillation (b)the maximum acceleration of the mass (c) The maximum speed of the mass. Ans- 3.2 ; 8.1 ; 0.4

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