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Class 11  »  Physics  »  Oscillations

Energy in SHM - UNSOLVED PRACTICE SET

Class 11

Chapter: Oscillations | Topic: Energy in SHM

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Class 11

ENERGY IN SHM - UNSOLVED PRACTICE SET

Topic: Energy in SHM

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. In SHM, the total mechanical energy is:

  1. Maximum at extreme position
  2. Maximum at mean position
  3. Constant at all positions
  4. Zero at mean position

Q2. The potential energy of a particle in SHM at displacement x is:

  1. (1/2)kx
  2. (1/2)kx²
  3. kx
  4. (1/2)mv²

Q3. The kinetic energy of a particle in SHM is maximum when the particle is at:

  1. Extreme position
  2. Mean position
  3. x = A/2
  4. x = A/√2

Q4. At what displacement in SHM is the kinetic energy equal to the potential energy?

  1. x = 0
  2. x = A/2
  3. x = A/√2
  4. x = A

Q5. The graph of kinetic energy versus displacement in SHM is:

  1. A straight line
  2. A parabola opening upwards
  3. A parabola opening downwards
  4. A sine curve

Q6. When you push a child on a swing in the school playground, the energy you give is stored as:

  1. Only kinetic energy at the highest point
  2. Only potential energy at the highest point
  3. Only kinetic energy at the lowest point
  4. Both kinetic and potential energy equally at all points

Short Answer Questions

Q7. Derive the expression for total energy of a particle executing SHM. Show that it is constant and proportional to the square of the amplitude.

Q8. Show that in SHM, the kinetic energy and potential energy vary with time as:

K.E. = (1/2)mω²A² sin²(ωt)

P.E. = (1/2)mω²A² cos²(ωt)

Q9. At what displacement is the kinetic energy twice the potential energy in SHM? Show your calculation.

Q10. Draw graphs of kinetic energy, potential energy, and total energy versus displacement for one complete cycle of SHM. Label all important points.

Q11. Explain why the average kinetic energy over one complete cycle in SHM equals the average potential energy over one complete cycle.

Q12. If the amplitude of SHM is doubled, how does the total energy change? How do the maximum kinetic energy and maximum potential energy change?

Long Answer Questions

Q13. Derive expressions for kinetic energy, potential energy, and total energy of a particle executing SHM. Show that:

(i) K.E. = (1/2)mω²(A² – x²)

(ii) P.E. = (1/2)mω²x²

(iii) Total energy E = (1/2)mω²A² = (1/2)kA²

Discuss how energy transforms between kinetic and potential forms during oscillation. Draw graphs showing the variation of K.E., P.E., and total energy with:

(a) Displacement x

(b) Time t

Q14. A particle of mass 0.1 kg executes SHM with amplitude 5 cm and angular frequency 10 rad/s.

(i) Calculate the total energy of the oscillation.

(ii) Calculate the kinetic and potential energies when the displacement is 3 cm.

(iii) At what displacement is the kinetic energy equal to 75% of the total energy?

(iv) Calculate the time interval between two successive instants when K.E. = P.E.

Q15. Consider two particles executing SHM with the same amplitude A and angular frequency ω, but with a phase difference of π/2.

(i) Write the equations of motion for both particles.

(ii) Show that when one particle has maximum kinetic energy, the other has maximum potential energy.

(iii) Calculate the total energy of the system (sum of both particles).

(iv) Explain why this system is analogous to the exchange of energy in a simple pendulum.

Numerical / Application-Based Problems

Q16. A block of mass 0.5 kg attached to a spring (k = 200 N/m) executes SHM with amplitude 10 cm.

(i) Calculate the total energy of the system.

(ii) Calculate the maximum speed of the block.

(iii) Calculate the kinetic energy when the block is at x = 6 cm.

(iv) Calculate the potential energy when the block is at x = 6 cm.

(v) At what positions is the speed equal to half the maximum speed? Calculate the energy at these positions.

Q17. A simple pendulum of length 1 m and mass 0.2 kg oscillates with an amplitude of 5° (small angle approximation valid).

(i) Calculate the time period of oscillation.

(ii) Calculate the maximum angular displacement in radians.

(iii) Calculate the total energy of the pendulum.

(iv) Calculate the speed of the bob at the lowest point.

(v) Calculate the height of the bob above the lowest point at the extreme position.

(Given: g = 9.8 m/s²)

Q18. In a school science fair, a student builds a "wave machine" using a series of 10 identical masses connected by springs. Each mass is 0.1 kg, and each spring has k = 50 N/m. One end mass is pulled 8 cm from equilibrium and released.

(i) Calculate the total energy stored in the system initially.

(ii) Calculate the maximum speed of the pulled mass.

(iii) As the wave propagates, the energy is shared among all masses. What is the maximum speed of any single mass when the energy is equally distributed?

(iv) The student observes that the amplitude gradually decreases. Where does the energy go? Name this phenomenon.

(v) If the student wants to maintain constant amplitude, what must she do? Name the phenomenon involved.


Total: 30 Marks | Time: 40 mins

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