Oscillations

Topics in this chapter

• SHM Equations And Kinematics
• Energy In SHM
• Spring-Mass Systems
• Pendulum Oscillations
• Damping And Special Oscillators

Cheat sheet

Practice questions

1. Question 1Q-682727

   Which of the following functions of time represents a simple harmonic motion?

   1. A.sin(omega t) - cos(omega t)
   2. B.sin^2(omega t)
   3. C.1 + omega t + omega^2 t^2
   4. D.e^{-omega t}
   See the answer and solution
2. Question 2Q-662F15

   A particle executes simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particle when its speed is half of its maximum speed is:

   1. A.A/2
   2. B.\frac{\sqrt{3}}{2} A
   3. C.A/\sqrt{2}
   4. D.\frac{A}{\sqrt{3}}
   See the answer and solution
3. Question 3Q-0DFE33

   A simple pendulum of length $L$ and mass $m$ is suspended in a lift that is accelerating upward with an acceleration $a$. The time period of small oscillations of this pendulum is:

   1. A.2\pi \sqrt{\frac{L}{g - a}}
   2. B.2\pi \sqrt{\frac{L}{g + a}}
   3. C.2\pi \sqrt{\frac{L}{g}}
   4. D.2\pi \sqrt{\frac{L}{\sqrt{g^2 + a^2}}}
   See the answer and solution
4. Question 4Q-A1BDDC

   The potential energy of a particle of mass $0.1\text{ kg}$ executing simple harmonic motion is given by $U = 5x^2\text{ J}$, where $x$ is displacement in meters. The frequency of oscillation is:

   1. A.\frac{5}{\pi}\text{ Hz}
   2. B.\frac{10}{\pi}\text{ Hz}
   3. C.\frac{\sqrt{5}}{\pi}\text{ Hz}
   4. D.\frac{5}{2\pi}\text{ Hz}
   See the answer and solution
5. Question 5Q-277A8B

   Two identical springs of spring constant $k$ are connected in series. The effective spring constant of the combination is:

   1. A.2k
   2. B.k/2
   3. C.\sqrt{2}k
   4. D.k/4
   See the answer and solution