A particle is making simple harmonic motion along the $\mathrm{X}$-axis. If at a distances $\mathrm{x}_{1}$ and $\mathrm{x}_{2}$ from the mean position the velocities of the particle are $v_{1}$ and $v_{2}$ respectively. The time period of its oscillation is given as :
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{x}_{2}^{2}+\mathrm{x}_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}}$
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{x}_{2}^{2}+\mathrm{x}_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}}$
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{x}_{2}^{2}-\mathrm{x}_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}}$
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{x}_{2}^{2}-\mathrm{x}_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}}$
Correct Option: , 4
$v^{2}=\omega^{2}\left(A^{2}-x^{2}\right)$
$\mathrm{A}^{2}=\mathrm{x}_{1}^{2}+\frac{\mathrm{v}_{1}^{2}}{\omega^{2}}=\mathrm{x}_{2}^{2}+\frac{\mathrm{v}_{2}^{2}}{\omega^{2}}$
$\omega^{2}=\frac{v_{2}^{2}-v_{1}^{2}}{x_{1}^{2}-x_{2}^{2}}$
$T=2 \pi \sqrt{\frac{x_{1}^{2}-x_{2}^{2}}{v_{2}^{2}-v_{1}^{2}}}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,