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Page 1 Numerical Q.1 A particle of mass 1 kg is hanging from a spring of force constant 100 Nm -1 . The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is ?? ?? The value of x is _____________. 31st Aug Morning Shift 2021 Q.2 Two simple harmonic motion, are represented by the equations Ratio of amplitude of y 1 to y 2 = x : 1. The value of x is ______________. 27st Aug Evening Shift 2021 Q.3 Two simple harmonic motions are represented by the equations 26st Aug Evening Shift 2021 Page 2 Numerical Q.1 A particle of mass 1 kg is hanging from a spring of force constant 100 Nm -1 . The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is ?? ?? The value of x is _____________. 31st Aug Morning Shift 2021 Q.2 Two simple harmonic motion, are represented by the equations Ratio of amplitude of y 1 to y 2 = x : 1. The value of x is ______________. 27st Aug Evening Shift 2021 Q.3 Two simple harmonic motions are represented by the equations 26st Aug Evening Shift 2021 Q.4 A particle executes simple harmonic motion represented by displacement function as 27th July Evening Shift 2021 Q.5 A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60 ° to the vertical will be (g = 10 m/s 2 ) ____________ m/s. 27th July Morning Shift 2021 Q.6 A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1 ?? The value of 'a' to the nearest integer is _________. 18th Mar Morning Shift 2021 Q.7 Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is where value of x is ___________. (Round off to the Nearest Integer) Page 3 Numerical Q.1 A particle of mass 1 kg is hanging from a spring of force constant 100 Nm -1 . The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is ?? ?? The value of x is _____________. 31st Aug Morning Shift 2021 Q.2 Two simple harmonic motion, are represented by the equations Ratio of amplitude of y 1 to y 2 = x : 1. The value of x is ______________. 27st Aug Evening Shift 2021 Q.3 Two simple harmonic motions are represented by the equations 26st Aug Evening Shift 2021 Q.4 A particle executes simple harmonic motion represented by displacement function as 27th July Evening Shift 2021 Q.5 A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60 ° to the vertical will be (g = 10 m/s 2 ) ____________ m/s. 27th July Morning Shift 2021 Q.6 A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1 ?? The value of 'a' to the nearest integer is _________. 18th Mar Morning Shift 2021 Q.7 Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is where value of x is ___________. (Round off to the Nearest Integer) 17th Mar Morning Shift 2021 Q.8 Time period of a simple pendulum is T. The time taken to complete 5 8 scillations starting from mean position is ?? ?? T The value of a is _________. 26th Feb Evening Shift 2021 Q.9A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is The value of x is __________. 26th Feb Evening Shift 2021 Q.10 A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm. 24th Feb Evening Shift 2021 Page 4 Numerical Q.1 A particle of mass 1 kg is hanging from a spring of force constant 100 Nm -1 . The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is ?? ?? The value of x is _____________. 31st Aug Morning Shift 2021 Q.2 Two simple harmonic motion, are represented by the equations Ratio of amplitude of y 1 to y 2 = x : 1. The value of x is ______________. 27st Aug Evening Shift 2021 Q.3 Two simple harmonic motions are represented by the equations 26st Aug Evening Shift 2021 Q.4 A particle executes simple harmonic motion represented by displacement function as 27th July Evening Shift 2021 Q.5 A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60 ° to the vertical will be (g = 10 m/s 2 ) ____________ m/s. 27th July Morning Shift 2021 Q.6 A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1 ?? The value of 'a' to the nearest integer is _________. 18th Mar Morning Shift 2021 Q.7 Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is where value of x is ___________. (Round off to the Nearest Integer) 17th Mar Morning Shift 2021 Q.8 Time period of a simple pendulum is T. The time taken to complete 5 8 scillations starting from mean position is ?? ?? T The value of a is _________. 26th Feb Evening Shift 2021 Q.9A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is The value of x is __________. 26th Feb Evening Shift 2021 Q.10 A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm. 24th Feb Evening Shift 2021 Numerical Answer Key 1. Ans. (8) 10. Ans. (2) 2. Ans. (1) 3. Ans. (2) 4. Ans. (2) 5. Ans. (2) 6. Ans. (6) 7. Ans. (2) 8. Ans. (7) 9. Ans. (3) Numerical Explanation Ans 1. Page 5 Numerical Q.1 A particle of mass 1 kg is hanging from a spring of force constant 100 Nm -1 . The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is ?? ?? The value of x is _____________. 31st Aug Morning Shift 2021 Q.2 Two simple harmonic motion, are represented by the equations Ratio of amplitude of y 1 to y 2 = x : 1. The value of x is ______________. 27st Aug Evening Shift 2021 Q.3 Two simple harmonic motions are represented by the equations 26st Aug Evening Shift 2021 Q.4 A particle executes simple harmonic motion represented by displacement function as 27th July Evening Shift 2021 Q.5 A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60 ° to the vertical will be (g = 10 m/s 2 ) ____________ m/s. 27th July Morning Shift 2021 Q.6 A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1 ?? The value of 'a' to the nearest integer is _________. 18th Mar Morning Shift 2021 Q.7 Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig. 1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is where value of x is ___________. (Round off to the Nearest Integer) 17th Mar Morning Shift 2021 Q.8 Time period of a simple pendulum is T. The time taken to complete 5 8 scillations starting from mean position is ?? ?? T The value of a is _________. 26th Feb Evening Shift 2021 Q.9A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is The value of x is __________. 26th Feb Evening Shift 2021 Q.10 A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm. 24th Feb Evening Shift 2021 Numerical Answer Key 1. Ans. (8) 10. Ans. (2) 2. Ans. (1) 3. Ans. (2) 4. Ans. (2) 5. Ans. (2) 6. Ans. (6) 7. Ans. (2) 8. Ans. (7) 9. Ans. (3) Numerical Explanation Ans 1. Ans 2. Ans 3. Ans 4.Read More
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FAQs on JEE Mains Previous Year Questions (2025)): Oscillations - Chapter-wise Tests for JEE Main & Advanced
| 1. What are the key concepts of oscillations that are frequently tested in JEE Mains? |  |
Ans. Key concepts of oscillations include simple harmonic motion (SHM), damped oscillations, forced oscillations, resonance, and the mathematical representation of oscillatory motion. Understanding the energy transformations in oscillations, the oscillation frequency, and the effects of damping and driving forces are critical for solving questions.
| 2. How do you differentiate between simple harmonic motion and damped oscillations in JEE Mains questions? | |
Ans. Simple harmonic motion (SHM) is characterized by a restoring force proportional to the displacement and results in constant amplitude, while damped oscillations involve a gradual decrease in amplitude over time due to energy loss (e.g., through friction). JEE questions may ask to identify properties of each type or calculate parameters such as frequency and amplitude in both scenarios.
| 3. What formulas related to oscillations should I memorize for JEE Mains? | |
Ans. Key formulas include:
1. For SHM: \( T = 2\pi\sqrt{\frac{m}{k}} \) (Period),
2. \( v = A\omega \cos(\omega t + \phi) \) (Velocity),
3. \( a = -A\omega^2 \cos(\omega t + \phi) \) (Acceleration),
4. Energy in SHM: \( E = \frac{1}{2} k A^2 \).
Memorizing these and understanding their derivations can help in solving problems efficiently.
| 4. What types of oscillation problems are commonly found in previous JEE Mains exams? | |
Ans. Common types of problems include calculations of frequency and period of oscillators, energy calculations in SHM, determining the effect of damping on oscillation amplitude, and scenarios involving coupled oscillators. Questions often test conceptual understanding through real-life applications, such as springs and pendulums.
| 5. How can I effectively prepare for oscillation-related questions in JEE Mains? | |
Ans. Effective preparation includes practicing previous years’ questions, understanding the derivations of key formulas, and solving numerical problems. Additionally, visualizing oscillation concepts through diagrams and simulations can enhance comprehension. Group study and discussing problems with peers can also aid in clarifying doubts and reinforcing learning.
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